Acoustic distance measurement (ADM) has been proposed as an accurate method by which to measure distances. The ADM method is based on the phase interference between the transmitted and reflected signals. However, the presence of ambient noise degrades the ranging performance. In previous studies, the noise component has been reduced by using three microphones in a noisy environment and applying independent component analysis or generating two difference signals from three observed data. The present paper describes a new, more compact, and practical method by which to reduce the ambient noise and perform ranging using only two adjacent microphones. Specifi-cally, the noise component is reduced by generating a difference signal between the two observations in a noisy environment. Then, the distance is estimated by applying the cross-spectrum method with the difference signal as the input and one of the observed signals as the output. Furthermore, the influence of noise is reduced by applying mask processing to the obtained result. The effectiveness of the proposed method was confirmed in a real room for a signal-to-noise ratio (SNR) of −10 dB. The results showed that the SNR for the difference signal was improved and the estimated distance agreed well with the true value, indicating the effectiveness of the proposed method.

The acoustic distance measurement (ADM) method based on phase interference between transmitted and reflected signal has been proposed as a method to accurately measure the distance. However, since its performance is deteriorated by ambient noise. In the previous study, complex ICA(Independent Component Analysis) was applied using adjacent 3ch microphone to reduce the noise. Although ICA achieves high performance for the noise reduction, it is not too practical method because of its high computational cost. This paper describes a practical method to reduce ambient noise in the ADM using adjacent 3ch observations. Concretely, the noise component is reduced by generating two difference signals among three signals of 3ch observations in the noisy environment. Then, the ADM using the crossspectrum method is applied to them. The difference signals can be obtained with a small computational cost. The validity of the proposed method is confirmed in the actual room under the condition where the SNR ratio is -10dB. As a result, the SNR is improved to 10.5 dB, demonstrating the validity of the proposed method.

Under ideal conditions with low noise, the acoustic distance measurement (ADM) method using the cross-spectrum for adjacent 2ch observations shows sufficient distance estimation performance. Increasing noise will deteriorate the distance estimation performance. To reduce noise, even if complex ICA is applied to adjacent 2ch noisy observations, sufficient separation performance for distance measurement cannot be exhibited, because the microphones are too close. Thus, if the ADM method using the cross-spectrum is applied to the separated signals of the adjacent 2ch noisy observations, an incorrect distance near 0 m is estimated because of the effect of measurement system. Therefore, by increasing the number of microphones (which increases information and can be expected to improve the separation performance), and applying complex ICA to improve the separation performance, ADM using the cross-spectrum for the new separation signals is proposed. This method enables us to obtain distance estimation that eliminates both environmental noise and the effect of the measurement system. The validity of the proposed method is also verified with the experiment of the actual distance measurement. As a result, it was found that the distance 1 m to the target can be measured under the noise of SNR (Signal to Noise Ratio) -10 dB.

© 2020, ICIC International. All rights reserved. In various fields, the distance to a target is important information. An acoustic distance measurement (ADM) method based on interference between transmitted and reflected waves using audible sound has been proposed. Environmental noise inevitably contaminates observations, and countermeasures against noise are indispensable. Synchronous addition is a method of reducing noise, but this method requires multiple measurements, and correct results cannot be obtained if the sound environment changes. There is also an attempt to reduce noise based on independent component analysis (ICA) using two-channel (2ch) observation signals. In the present study, the goal is to perform distance estimation in a single measurement under high noise. Signal separation by complex ICA using 2ch microphones (mic’s) is less accurate when the mic’s are closer than the sampling interval. In other words, it is difficult to obtain an accurate separation result only using two mic’s. Therefore, ICA is applied to two sets of two signals among 3ch observation signals with one additional mic, and after restoring two ranging signals to the mic positions, the ADM method using the cross-spectral method is applied. Finally, in order to confirm the effectiveness of the proposed method, this method is applied to an actual sound environment.

This paper describes a noise reduction method for acoustic distance measurement using cross spectrum between 2ch observations, constructing analytic signal based on cosine and sine linear chirp sound. Specifically, synchronous addition is appplied to observed signals themselves or to their cross spectrum.

The distance to a target is important information in various engineering fields. When measuring the distance to a target using audible sound, in general, an impulsive sound is transmitted toward the target and the time difference between the transmitted and reflected waves is obtained to determine the distance. However, this method cannot be applied to short distances where a reflected wave is buried in a transmitted wave. On the other hand, in the field of microwave radar, this distance measurement method has been proposed for plural targets, and can be applied to distances close to 0 m (i.e., a standing-wave radar). We have extended this distance measurement method so as to measure precisely the distance to the target in ranges close to 0 m by applying the principle of the standing wave radar to distance measurement using a sound signal. In this paper, first we will explain the principle of acoustical distance measurement methods based on phase interference using audible sound, and then by introducing an analytic signal, we describe in detail an acoustical distance measurement method, especially for a target that exists at a distance of around 0 m. Simulation results and experimental results are also shown.

Ultrasonic waves were very often used to measure the distance to a target. Authors proposed a distance measurement method based on phase interference between the transmitted and reflected audible sounds. This paper describes a new trail on the distance measurement using ultrasonic waves for close range by using a single transducer.

The sound source localization problem (identifying the distance and the direction from sound source) has been important in various engineering fields and many approaches have been developed, e.g., MUSIC (MUltiple SIgnal Classification). However, they often require a microphone array with multiple microphone elements to obtain such information. Meanwhile, since the distance to a target is also important, many distance measurement methods with sound have been proposed. We proposed an acoustic distance measurement (ADM) method based on interference between transmitted and reflected waves, which could measure distance at a short range. Existing ADM methods based on interference make errors due to the measuring system from the loudspeaker to the microphone. To remove the effect of the measuring system, a cross-spectral analysis was applied to the observed wave and the pseudo-observed wave, convolving the transmitted wave with the impulse response of the measuring system a priori measured. Attaching a microphone to a target causes multiple reflections (interference between the sound source and the target). This paper describes a method based on the phase interference to estimate the distance between a sound source and a target (reflector), using a single-channel cross-spectrum between the observed and the pseudo-observed waves. The validity and effectiveness of the proposed method is confirmed through simulation and experiment.

The acoustic distance measurement(ADM) method based on phase interference has been proposed. However, it becomes difficult for ADM to measure the distance to target shorter than distance resolution. Though the principled method for close range has been also proposed by introducing analytic signal, the measurement performance was degraded by the DC component of the power spectrum. This paper describes a new trail on the ADM with 2 ch microphones for very close range measurement by estimating and removing the DC component.

The distance estimation method based on interference of linear chirp sound has been proposed. However, the measurement performance was degraded by additional noise. In this paper, we expand the method to a method that is robust to noisy environments by introducing a concept of synchronous addition and spectral subtraction. Finally, we confirm the validity and effectiveness of the expanded method through experiments.

In many engineering fields, distance to target is very important information. Typical distance measurement methods use the time delay between transmitted and reflected waves, but it is difficult to estimate short distances. A method for measuring short distances using a standing wave generated by phase interference of transmitted and reflected waves is known in the field of microwave radar. This method is given in a very simple form in which the distance between the microphone and target is estimated as the peak value of the range spectrum, which can be obtained from the Fourier transform of the power spectrum of the observed wave. However, since the minimum measurable distance depends on the bandwidth of the transmitted wave, measurement of shorter distances requires greater bandwidth of the transmitted wave. This paper describes a new distance estimation method that is effective from 0 m based on the phase interference of transmitted and reflected audible sound. Specifically, we introduce an analytic signal instead of the power spectrum and examine the validity and effectiveness of our method by applying it to an actual sound field. (C) 2014 Wiley Periodicals, Inc.

Parametric loudspeaker can form an acoustic beam with sharper directivity by using multiple small ultrasonic transducers. In recent years, acoustic beam steering methods based on delay-processing for multiple small ultrasonic transducers is proposed. However, in these methods, spatial aliasing in ultrasonic waves has not been focused. Therefore, in this paper, we investigate the relationship between the spatial aliasing of ultrasonic waves and the acoustic beam of audible sounds. In addition, we propose acoustic beam steering with parametric loudspeaker by individual delay-filtering for carrier and sideband waves.

Patients who have difficulty moving their muscles freely require support for various situations that occur in everyday life. A controllable robot arm without using muscles may make the patient's quality of life improve. By using a brain-computer interface (BCI), control of the robot arm is possible by thought alone. Therefore, we have constructed several robot arms with an ultrasonic range finder and a web camera for BCI system. By utilizing these devices, collisions between the robot arm and the user could be avoided and control could be partially automated. The distance is very important information in the system. In the present work, an acoustic distance measurement (ADM) device was used. It consists of equipment with easy acquisition and does not need an electronic circuit which is in the ultrasonic range finder. It is a new device and has a possibility of simplifying the ADM device.

Since the distance to target is very important information, we have proposed an acoustic distance measurement (ADM) method using a standing wave, which is generated by interference between transmitted and reflected waves. However, the amplitude-frequency characteristics of the measuring system between the microphone and the loudspeaker are not considered, but these characteristics cannot be ignored in a real environment. To remove the effect of the measuring system, our previous methods required a 2ch microphone or two measurements with targets and without targets. This paper describes a new ADM method considering a movement of transmitting-and-receiving system composed of 1ch microphone and loudspeaker. Finally, we examine the validity and effectiveness of our method by applying it to an actual sound field.

In a number of engineering fields, information on the distance to the target is very important. We previously proposed an acoustic distance measurement method based on interference between the transmitted and reflected waves, which can be used for distance measurement over a short range. In the previously proposed method, a sound source of the transmitted wave must be known in advance. In the present paper, we propose a new acoustic distance measurement method based on phase interference obtained using the cross-spectral method with adjacent microphones, which does not require the condition that a sound source of the transmitted wave is known. Finally, we confirmed the validity and effectiveness of the newly proposed method through both computer simulation and evaluation experiment in a real environment.

In a number of engineering fields, information on the distance to the target is very important. We previously proposed an acoustic distance measurement method based on interference between the transmitted and reflected waves, which can be used for distance measurement over a short range. The previously proposed method requires equipment such as a loudspeaker and a microphone for cancellation processing of background components due to the spectrum of the transmitted wave and the transfer function of the measurement system in real environments. Therefore, in the previously proposed method, a sound source of the transmitted wave must be known in advance. In the present paper, we propose a new acoustic distance measurement method based on phase interference obtained using the cross-spectral method with stereo microphones, which does not require the condition that a sound source of the transmitted wave is known. The conventional cross-spectral method requires a measuring remote microphone and a reference microphone to be placed near a loudspeaker, meanwhile the proposed method requires stereo microphones to be placed near a sound source. Finally, we confirmed the validity and effectiveness of the newly proposed method through computer simulations and evaluation experiments in real environments. © 2013 The Acoustical Society of Japan.

Beamforming with a microphone-array is an ideal candidate for distant-talking speech recognition. An adaptive beamformer can achieve beamforming with a small microphone-array, but it had difficulty extracting distant-moving speech and reducing moving noises, because it must rapidly train long multiple-channel adaptive filters by using observed noises with a microphone-array. However, if positions of both talkers and noises can be estimated, adaptive filters may not need to be trained in real noisy environments. Therefore, we propose a multiple-nulls-steering beamformer based on both talker and noise localization that does not require adaptive training with observed noises. Finally, we confirmed the validity and effectiveness of the proposed method through computer simulations and evaluation experiments in real noisy environments. © 2013 The Acoustical Society of Japan.

In many engineering fields, distance to target is very important information. Typical distance measurement methods use time delay between transmitted and reflected waves, but it is difficult to estimate short distance. On the other hand, a method for measuring short distances using a standing wave, which is generated by phase interference of transmitted and reflected waves, is known in the field of microwave radar. This method is given in a very simple form such that the distance between microphone and target is estimated as a peak value of the range spectrum, which can be obtained by Fourier transform of the power spectrum of the observed wave. However, since the minimum measurable distance depends on the bandwidth of the transmitted wave, the shorter distance measurement requires the wider bandwidth of the transmitted wave. This paper describes a new distance estimation method measurable from 0m based on the phase interference of transmitted and reflected audible sound. More concretely, we introduce an analytic signal instead of the power spectrum and examine the validity and effectiveness of our method by applying it to an actual sound field. © 2012 The Institute of Electrical Engineers of Japan.

In robot sensors and security systems, both range and velocity to a moving target are very important. In this paper, we propose a method to estimate both range and velocity based on the phase interference of subband-divided and timedelayed impulse sound to a moving target in a short range. Evaluation experiments revealed that the proposed method was valid because the proposed method was measurable both range and velocity to a moving target. © 2012 The Institute of Electrical Engineers of Japan.

Since the distance to target is very important information, we have proposed an acoustic distance measurement using a standing wave, which is generated by interference between transmitted and reflected waves. This method is given in a very simple form such that the distance between microphone and target is estimated as a peak value of the range spectrum (i.e., the absolute value of Fourier transform with respect to the power spectrum of the observed wave). However, to measure the short distance, the wide bandwidth of the transmitted wave is required. This paper describes a new distance estimation method measurable from 0 m based on the interference between transmitted and reflected audible sound, especially using only a single microphone (i.e., single channel observations). More concretely, we introduce an analytic signal instead of the power spectrum and examine the validity and effectiveness of our method through computer simulation and by applying it to an actual sound field with a band-limited impulse sound. © 2012 IEEE.

The distance to talkers is very important information for both hands-free speech interfaces and nursing-care robots. We have proposed an acoustic distance measurement method based on interference between the transmitted and reflected waves, which can measure distance in a short range. In the present paper, we propose an acoustic distance measurement method based on interference of speech presented by a dialogue system. In a dialogue system, dry sources of presented speech are known. Therefore, we can easily perform voice activity detection (VAD) for presented speech using a phoneme segmentation with a hidden Markov model. The proposed method estimates the distance to talkers in speech segments using the results of VAD. Finally, we confirmed the effectiveness of the proposed method through experiments in real environments. © 2012 IEEE.

In many engineering fields, the distance to target is very important information. In a typical method, the distance is estimated by measuring the time delay between transmitted and reflected waves. However, it is difficult to estimate short distances with a method like this. In the field of microwave radar, a method using standing waves to measure short distances and multiple targets is known. We have applied this method to distance estimation using audible sound and have shown the validity of this method by our simulations and experiments. In this paper, we present a prototype system for distance estimation in which this method is implemented, and evaluate the performance of this system by experiments in an actual sound field. (C) 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 177(2): 41-48, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21160

Distance to target is fundamental and very important information in numerous engineering fields. Many distance measurement methods using sound use the time delay of a reflected wave, which is measured in reference to the transmitted wave. This method, however, cannot measure short distances because the transmitted wave, which has not attenuated sufficiently by the time the reflected waves are received, suppresses the reflected waves for short distances. Therefore, we proposed an acoustic distance measurement method based on the interference between the transmitted wave and the reflected waves, which can measure distance in a short range. The proposed method requires a cancellation processing for background components due to the spectrum of the transmitted wave and the transfer function of the measurement system in real environments. We refer to this processing as background components cancellation processing (BGCCP). We proposed BGCCP based on subtraction or whitening. However, the proposed method had a limitation with respect to the transmitted wave or additive noise in real environments. In the present paper, we propose an acoustic distance measurement method based on the new BGCCP. In the new BGCCP, we use the calibration of a real measurement system and the whitening processing of the transmitted wave and introduce the concept of the cepstrum to the proposed method in order to achieve robustness. Although the conventional BGCCP requires the recording of the transmitted wave under the condition without targets, the new BGCCP does not have this requirement. Finally, we confirmed the effectiveness of the proposed method through experiments in real environments. As a result, the proposed method was confirmed to be valid and effective, even in noisy environments.

我々はこれまで,可聴音域に拡張した送信波と反射波の位相干渉に基づく近距離推定法について検討してきた.本研究では,対象物のある環境とない環境での同期収録信号をスペクトル減算することで,バックグラウンド要素を除去する音響測距法を検討する.

特定の場所の音環境を立体的に再現する技術として,頭部伝達関数(Head Related Transfer Function:HRTF)を事前に計測して適用するバイノーラル方式と任意の位置にある複数の遠隔スピーカを利用するトランスオーラル方式が提案されている.バイノーラル方式はヘッドホンの着用が煩わしく,トランスオーラル方式は機器の個数や計算量の点で非常に複雑かつ大規模なシステムとなる問題がある.一方,我々はこれまで,スピーカとその近傍のマイクロホンで収録した直接音と反射音の位相干渉を利用した音響測距法を提案してきた.この音響測距法は,スピーカと受聴者の耳元間の距離計測に利用できる.この距離情報とスピーカ配置を考慮することで,トランスオーラル方式と比べて小規模な立体音場再現システムを実現できる可能性がある.そこで本研究では,受聴者の頭部の左右近傍に設置したスピーカ-マイクロホン対を利用した音響測距法に基づく立体音場再現手法を提案する.更に,理論の正当性を確認するための予備実験と,HRTFにより定位を付与した音楽による主観評価実験を行うことで,提案手法の有効性を確認する.

In many engineering fields, distance to targets is very important. General distance measurement method uses a time delay between transmitted and reflected waves, but it is difficult to estimate the short distance. On the other hand, the method using phase interference to measure the short distance has been known in the field of microwave radar. Therefore, we have proposed the distance estimation method based on interference between transmitted and reflected audible sound, which can measure the distance between microphone and target with one microphone and one loudspeaker. However, the distance measurement performance of the proposed method was degraded by additional noise in noisy environment. In this paper, the acoustic distance measurement method based on the interference between the transmitted wave and the reflected waves is expanded to a noise-robust method in a noisy environment. In order to measure distance in a low-signal-to-noise ratio (low-SNR) environment, we introduce a concept from synchronous addition and spectral subtraction to the proposed method. Evaluation experiments in a real environment reveal that the proposed method was valid and effective because the proposed method could measure distance in a low-SNR environment. © 2011 The Institute of Electrical Engineers of Japan.

For tele-conference systems or voice-controlled systems, it is very important that distant-talking speeches with a high quality are separately extracted in environments including multiple talkers and noises. Beamforming with microphone-array is an ideal candidate for overcoming this problem. In reverberant environments, the beamforming technology had difficulty in extracting distant-moving speeches and in reducing moving noises because conventional methods must rapidly train multiple-channel adaptive filters with long filter length by using observed noises with microphone-array. However, if positions of talkers and noises can be estimated, it may be not necessary that adaptive filters are trained in real noisy environments. Therefore, we propose the multiple-nulls-steering beamformer based on talkers and noises localization, which doesn't require training with observed noises. The proposed method applies rapidly multiple pre-designed null-steering-filters without observed noises on the basis of talkers and noises localization. Also, multiple null-steering-filters are trained on the basis of positional information by talkers and noises localization and those mobility predictions. The proposed method utilizes the integrating system of loudspeaker and microphone-array. In the proposed method, positions of talkers are estimated by the acoustic distance measurement method based on interference, and positions of noises are estimated by the cross-power spectrum phase analysis method. Additionally, in order to apply null-steering-filters to observed signals in real environments, the proposed method performs calibration of variations in each channel by using loudspeaker and microphone-array. Finally, we will confirm the effectiveness of the proposed method through real experiments. Copyright © (2011) by the Institute of Noise Control Engineering.

In many engineering fields, the distance to target is fundamental and very important information. Acoustical signals, such as audible sound or ultrasound, often play an essential role in measurement of distance. To measure distance, the time delay of the reflected wave measured with reference to the transmitted pulse wave, that is, the time-of-flight (TOF), is typically used. However, this method cannot measure short distances because the transmitted wave, which has not attenuated enough at the time of reception of the reflected waves, suppresses the reflected waves for a short distance. Meanwhile, in microwave radar research, a novel method using standing waves has been recently proposed in order to measure the distances to multiple targets, even if short. We apply the fundamental principle of this method to the estimation of short distances for multiple targets using audible sound. In this paper, we focus our attention on audible band-limited noise. To verify the validity and effectiveness of our method, we perform computer simulations and experiments. It is confirmed that short distances to multiple targets, such as the distances to two targets located 0.1 and 1 m away, can be estimated properly by our method. (C) 2010 Wiley Periodicals, Inc. Electron Comm Jpn, 93(7): 53-60, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10248

In many engineering fields, distance to targets is very important. General distance measurement method uses a time delay between transmitted and reflected waves, but it is difficult to estimate the short distance. On the other hand, the method using phase interference to measure the short distance has been known in the field of microwave radar. Therefore, we have proposed the distance estimation method based on interference between transmitted and reflected audible sound, which can measure the distance between microphone and target with one microphone and one loudspeaker. In this paper, we propose talker localization method based on distance estimation using phase interference. We expand the distance estimation method using phase interference into two microphones (microphone array) in order to estimate talker position. The proposed method can estimate talker position by measuring the distance and direction between target and microphone array. In addition, talker's speech is regarded as a noise in the proposed method. Therefore, we also propose combination of the proposed method and CSP (Cross-power Spectrum Phase analysis) method which is one of the DOA (Direction Of Arrival) estimation methods. We evaluated the performance of talker localization in real environments. The experimental result shows the effectiveness of the proposed method. © 2010 the Institute of Electrical Engineers of Japan.

「怒り」，「喜び」，「悲しみ」などの感情を表現した自然音声の音響的特徴を「韻律（声の大きさ，高さ，発話速度の総称）」という視点から解析してきた。筆者らの研究の特徴は，より微妙なニュアンスの特徴まで調べることを目的に，それぞれの感情を，感情を含まない「平常」のほか，「弱い」，「中程度」，「強い」の4段階の度合に分類して解析を行い，それぞれの特徴を体系的に明らかにしてきたことである。
会話によるコミュニケーションにおいて，話者の心の内面にある感情がそのまま発声に反映され，更にそのまま聞き手に伝わるとは限らない。
本研究の目的は，(1)このような話者の内面の感情（話者の意図）がどの程度正しく聞き手に伝わるのか，(2)どのような表現のときに話者の意図した感情が正しく聞き手に伝わりやすいのか，を定量的に明らかにすることである。
そこでまず，発話の意図がどの程度聞き手の聴覚的印象と一致しているかを調

In many engineering fields, distance to target is very important information. As a typical method, distance is estimated by measuring time delay between transmitted and reflected waves. However, it is difficult to estimate short distance by a method like this. On the other hand, a method using standing wave to measure short distances has been known in the field of microwave radar. We have applied this method to distance estimation using audible sound and shown the validity of that through our simulations and experiments. In this paper, we present the prototype system for distance estimation in which this method is implemented, and evaluate the performance of this system by experiments in actual sound field. © 2009 The Institute of Electrical Engineers of Japan.

Distance to target is fundamental and very important information in many engineering fields. In some applications sound is often used to measure distances to targets. For this purpose, the time delay of reflected wave is typically used. This method, however, can not measure short distance because the transmitted wave, which has not attenuated enough as of reception of reflected waves, suppresses the reflected waves for short distance. Meanwhile, in the research field of microwave radar, to measure distances to multiple targets even if they are short, a novel method by using standing wave has been recently proposed. In this paper, we apply the fundamental principle of this method to measurement of short distance for multiple targets using sound wave. Specifically, we focus our attention on audible band-limited signal with random phases. To verify the validity and effectiveness of our method, we perform computer simulations and experiments. As a result, it has been confirmed that short distances to multiple targets, such as the distances of two targets located at 0.5 m and 1 m, can be measured by our method. © 2009 The Acoustical Society of Japan.

In many engineering fields, distance to target is fundamental and very important information. Acoustical signal, such as audible sound or ultrasonic, often plays an essential role in measurement of distance. To measure distance, the time delay of reflected wave measured with reference to transmitted pulse wave, i.e. time-of-flight (TOF) is used typically. This method, however, can not measure short distance because the transmitted wave, which has not attenuated enough as of reception of reflected waves, suppresses the reflected waves for short distance. Meanwhile, in the research field of microwave radar, to measure distances to multiple targets even if short, a novel method by using standing wave has been recently proposed. We apply the fundamental principle of this method to estimation of short distance for multiple targets using audible sound. In this paper, we focus our attention on audible band-limited noise. To verify the validity and effectiveness of our method, we perform computer simulations and experiments. As a result, it has been confirmed that short distances to multiple targets, such as the distances to two targets located at 0.1m and 1m, can be estimated properly by our method.

In the research field of microwave radar, a range finding method based on standing wave is known to be effective for measuring short distances. In this paper, we focus our attention on audible sound and fundamentally examine the distance estimation method in which acoustical standing wave is used.

It is known that sound field in a one-dimensional duct can be simply expressed on the basis of a transmission line model. Authors have proposed ANC system probing sound pressures at arbitrary two points of the transmission line, though only the two-point probing for sound pressure between the primary and the secondary sources has been utilized for the sake of simplification of ANC circuit. The one-dimensional acoustic duct can be expressed by a transmission line model commonly used in the study of microwave waveguideh. The authors have also analyzed the sound decaying property in a case when the sound propagates through random media based on the circuit theory. The computer simulation demonstrates the damping effect for random media. However, producing the sound field according to this method corresponds to a random change of medium itself in one-dimensional duct and it must be unrealistic. Along the transmission line model with the existence of random media, this paper describes the sound decaying property of the random loadings using the equivalent circuit representation for a sound duct. Finally the validity of the proposed theory is confirmed through computer simulation.

In order to establish an objective approach for evaluating human emotions, Emotional Spectrum Analysis Method (ESAM) has been proposed by Dr. T. Musha et al. It is possible to estimate emotion spectrums with four basic emotional states (i.e., anger/stress, joy, sadness and relaxation) by using ESAM and the measured data of brain waves. Now, we pay attention to the emotional evaluation of music sounds. More specifically, this paper describes the influence of a change of music sounds with different tones (from a minor scale to a major scale) on human emotions. The brain waves for six subjects are measured by electroencephalogram (EEG). Each emotion spectrum can be estimated by using the emotion spectrum analysis system developed by Brain Functions Laboratory, Inc. based on ESAM. The effectiveness of ESAM is experimentally confirmed by applying it to the emotion evaluation problem of the above two kinds of music sounds. We find out the possibility of ESAM for the objective evaluation in the field of music.

本研究では，風速から風雑音を推定し，その風雑音を風雑音下の観測信号から除去することにより信号のみを抽出する簡便な手法を提案する．具体的には，風速を入力とする線形・非線形のシステムモデルを用い風雑音の音圧レベルをまず推定する．ついで，その推定した風雑音を観測信号から音のエネルギースケールで減算し，風雑音成分を除去する．線形モデルとしてはMAフィルタ，非線形フィルタとしてニューラルネットワークを採用する．また，線形成分はMAフィルタで捉え，それからズレた非線形成分についてはニューラルネットワークで補正する組み合わせ手法も提案する．最後に，実際の風雑音混入下において音響信号を検出する問題に本手法を適用し，その有効性を検証した．(英文)

Sound decaying property in the random media using the equivalent circuit representation for a sound duct was described. The simulation of the random duct based on the fluctuating medium was performed. The sound field in one-dimensional random media was analyzed in terms of the equivalent circuit representation. It was shown that the exponential decay constant was approximately proportional to the variance of the random medium.

Active noise control (ANC) in a one-dimensional duct can be expressed in terms of a transmission line model. Thus, the proposed ANC system probes sound pressures at arbitrary two points of the transmission line, differing from a usual system such as Filtered-x. The frequency response function of ANC circuit is obtained and then the two-stage digital filter for control is realized. More concretely, the first stage filter generates the voltage and current at the secondary source position from the observations and the second one produces the secondary source. Finally the validity of the proposed theory is confirmed through simulation.

複数の混合音から複数の音源の位置を同定する手法を提案した。とくに今回は時間遅れを伴う混合を想定し、ブラインド分離により求まるパラメータを利用した。さらに逆フィルタ処理により信号のクリアな分離が可能となることも示した。（招待論文、英文）

近年脚光を浴びている独立成分分析（Independent Component Analysis; ICA）について、著者らの研究成果を中心に基礎から、とくに音響信号処理に関連して解説した。瞬時混合の場合だけでなく音響計測では無視できない畳み込み混合の場合にも焦点を当てた。

In the actual sound environment, the objective system often exhibits the non-Gaussian property, owing to physical, social and psychological factors. Many kinds of probability distributions have been proposed from various viewpoints to describe the probabilistic property of complicated random phenomena. Sometimes, a probability distribution of orthogonal series expansion type, which takes the well-known probability distribution (e.g., Gaussian, binomial distributions, etc.) as the first term and reflects the lower and higher order statistics in the expansion terms is also utilized. This paper describes a practical trial to choose the permissible order of series expansion, especially by introducing a pre-established tolerance range for the deviation of the theoretical cumulative probability from the experimental one. The minimal number of expansion terms can be rationally determined so as to satisfy the tolerance range. Finally, the effectiveness of this method is experimentally confirmed by applying it to the environmental noise.

Recently, the problem of independent component analysis and/or blind signal separation becomes a very popular and emerging field of research, because the problem contains many potential applications. In such a problem, a priori information we can. utilize is the statistical independency between source signals. In many actual fields, the independent component analysis must play an essential role but it also contains problems: it cannot be applicable to non-physical quantity like a human psychological or sensory one, etc. This paper proposes a fundamental trial of independent component analysis by introducing Fuzzy theory. More concretely, the parameters of unknown system are estimated on the basis of Fuzzy observations. Finally, the effectiveness of this method is confirmed through digital simulation.

In the actual situation, it is very difficult to evaluate the complicated sound environment only by using the lower order statistics of intensity such as Leq. In the actual acoustic measurement, a background noise always contaminates observation values and the statistics of the background noise are usually unknown. In this paper, the statistical independency between the acoustic signal and the background noise is introduced as an evaluation criterion to identify the sound insulation systems. That is, by considering the sound insulation wall as a linear system on an intensity scale, the system parameters are estimated on the basis of the statistical information from the lower to the higher orders, instead of employing the artificial evaluation criterion such as the least squares error method. Then, the output probability can be easily predicted by using the estimated parameters of the sound insulation system when the other input noise passes through the same insulation system. Finally, the validity and effectiveness of the proposed method are experimentally confirmed by applying it to the actually observed data.

This paper describes a new trial to estimate the statistical input-output relationship of complicated sound insulation systems in an actual situation when the input-output data are roughly observed due to the level-quantization mechanism of measuring equipment, especially from a practical viewpoint. Then, the output probability distribution for another kind of input can be predicted by using the estimated regression relationship. Finally, the effectiveness of the proposed method is experimentally confirmed by applying it to the actually observed data.

In this paper, a statistical electromagnetic (abbr., EM) interference study is constructed mainly from a theoretical viewpoint on the basis of N-dimensional random walk problem in multi-dimensional signal space. First, a characteristic function of the Hankel transform type matched to this EM environmental study is introduced especially in an extended form of D. Middleton's basic result. Then, the probability density function (abbr., pdf) is explicitly derived for the EM random fluctuation with a power scaled variable (or an effective value) measured by a receiver with a mean square operation. The proposed theory is verified by showing the agreement with one of D. Middleton's great researches as a special case of the proposed expressions. Moreover, the effectiveness of the proposed method is experimentally confirmed through an acoustic type simulation of EM environment and the application to a simplified actual EM environment with joint space-time non-Poisson interference as one of the same wave motion type environment as EM environment.

This paper proposes a prediction method for non-stationary time series data with time varying parameters. A modular structured type neural network is newly introduced for the purpose of grasping the changing property of time varying parameters. This modular structured neural network is constructed by the hierarchical combination of each neural network (NNT: Neural Network for Prediction of Time Series Data) and a neural network (NNW: Neural Network for Prediction of Weights). Next, we propose a reasonable method for determination of the length of the local stationary section by using the additive learning ability of neural networks. Finally, the validity and effectiveness of the proposed method are confirmed through simulation and actual experiments.

In the measurement of actual random phenomenon, the observed data often contain the fuzziness due to the existence of confidence limitation in measuring instruments, permissible error in experimental data, some practical simplification of evaluation procedure and a quantized error in digitized observation. In this study, by introducing the well-known fuzzy theory, a state estimation method based on the above fuzzy observations is theoretically proposed through an establishment of wide sense digital filter under the actual situation of existence of the background noise in close connection of the inverse problem. The validity and effectiveness of the proposed method are experimentally confirmed by applying it to the actual fuzzy data observed in an acoustic environment.

The noise fluctuation is very often measured in a quantized level form at a discrete time interval. By paying attention to this quantization procedure of the actual noise measurement, in this paper, a precise estimation method for the probability distribution form is proposed by using the roughly observed data with quantized levels. That is, we first introduce theoretically a general statistical orthonormal expression of the probability density function for the original noise level fluctuation of continuous level type before passing through the level quantization measurement mechanism. Based on this quantization mechanism and the averaging operation of statistical information, we propose a reasonable estimation method of the distribution parameters in the above statistical expression by using the statistical information on the roughly observed data. The original probability distribution form of the continuous noise level can be precisely estimated by substituting the estimated distribution parameters into the introduced probability expression of general type. On the basis of this estimation theory, a precise evaluation method for the Lx and Leq noise evaluation indices is proposed. The effectiveness of the proposed method is confirmed experimentally too by applying it to first the simulation experiment and then the actual road traffic noise data.

A practical and suboptimal estimation algorithm, proposed as a signal restoration method based on Bayes' theorem, resembles a previously reported method used to design a wide sense digital filter, especially for noisy and level-quantized observations. The proposed method utilizes linear and nonlinear correlation information between the unknown acoustic signal and the observation value (before quantization operation) by using quantized level observations. The effectiveness of the proposed theory is confirmed experimentally through the simulation technique and by applying it to the actual reverberation data contaminated by a background noise.

This paper describes a trial of evaluating the proper characteristics of multiple sound insulation systems from their output responses contaminated by unknown background noises, The unknown parameters of sound insulation systems are first estimated on the basis of the linear time series on an intensity scale, describing functionally the input-output relation of the systems. Then, their output probability distributions are predicted when an arbitrary input noise passes through these insulation systems.

This paper presents a practical prediction or transformation method from Lx data to Leq value, especially for the road traffic noise at night with a small traffic volume. The nonlinear relationship between Lx and Leq is grasped in principle by introducing a probabilistic neural network. Finally, the validity of the proposed method is experimentally confirmed too by applying it to the actually observed road traffic noise at night. © 1996, Acoustical Society of Japan. All rights reserved.

現実の音環境における不規則信号は、様々な環境要因により複雑な変動特性を示すのが常である。本論文では、このような実状況の環境騒音に対する統計的一評価手法を原理的に提案している。特に実用性に考察の主点を置き、ごく少数個のみのパラメータを持つ単純・標準化された結果を、まず理論的枠組みに採る。次に、単純から複雑への拡張原理に支えられた2種情報処理法として、ニューラルネットワークとファジー確率論理を採り上げ、現実の音環境における複雑さへも適用可能な形態へと方法論を拡張する。最後に音環境での実測データに適用することにより、方法論の有効性を3種の実際的場合へ適用して原理的に確認している。

騒音・振動環境分野では、自然要因の多様さや人間評価の非画一性に基づいて、様々な評価量が提案され、それぞれ固有な長短所を待ち合わせている。本研究では、L_x(x=5,50,95)評価量を一具体例にとり、各評価量間で説明変数から目的変数への一方向的な変換関係を求める回帰分析法とは異なり、互いに優劣なく双方向に変換可能な代表的一関連様式を見出す目的で主成分分析法にまず着目する。次いで、各L_x評価量間では本質的に非線形な関連様式を潜在させることから、線形関連様式を主とした公知の主成分分析法を非線形関連様式へ一般化できる一試みを、その原則論に力点をおいて提案する。更に、実L_xデータ間に適用しその実際的有効性をも実証する。

In the measurement of actual phenomena, the observed data often suffer from loss or distortion due to the limited dynamic range of the measurement instruments. This paper describes a new method of dynamical state estimation for stochastic systems, in a practical case in which the observed data fluctuates within a finite amplitude domain owing to the dynamic range of the measurement instrument. The state estimation method proposed for use with such incomplete observation data (with information loss or distortion) is a theoretically based improvement of the wide sense digital filter, for situations in which the data is contaminated by an external noise of arbitrary distribution type. A recurrence type estimation algorithm is explicitly derived in series expansion form from the Bayesian viewpoint, with the aim of utilizing hierarchically the linear and non-linear correlation information between the observed value and the unknown state variable. The proposed estimation theory is experimentally confirmed by applying it to a problem of background noise correction in room acoustics.

A specific signal in most of actual environmental systems fluctuates complicatedly in a non-Gaussian distribution form, owing to various kinds of factors. The nonlinearity of the system makes it more difficult to evaluate the objective system from the viewpoint of internal physical mechanism. Furthermore, it is very often that the reliable observation value can be obtained only within a definite domain of fluctuating amplitude, because many of measuring equipment have their proper dynamic range and the original random wave form is unreliable at the end of amplitude fluctuation. It becomes very important to establish a new signal processing or an evaluation method applicable to such an actually complicated system even from a functional viewpoint. This paper describes a new trial for the signal processing along the same line of the extended regression analysis based on the Bayes' theorem. This method enables us to estimate the response probability property of a complicated system in an actual situation, when observation values of the output response are saturated due to the dynamic range of measuring equipment. This method utilizes the series expansion form of the Bayes' theorem, which is applicable to the non-Gaussian property of the fluctuations and various kinds of correlation information between the input and output fluctuations. The proposed method is newly derived especially by paying our attention to the statistical information on the input-output data without the saturation operation instead of that on the resultantly saturated observation, differing from the well-known regression analysis and its improvement. Then, the output probability distribution for another kind of input is predicted by using the estimated regression relationship. Finally, the effectiveness of the proposed method is experimentally confirmed too by applying it to the actual data observed for indoor and outdoor sound environments.

既発表の拡張型回帰分析法の解析基盤となるベイズ定理が原理的に情報量規範と等価な解を生むことを積極的に利用して、操作面上ベイズ定理より柔軟な極値探索型の情報量規範を適用することにより、複雑な住環境騒音を実用的に評価できる新たな一回帰分析法を提案した。情報量規範として入出力間の条件付エントロピーを最小にする評価規範を導入し、確率近似法を援用して入出力データを逐次採取することによってシステム同定ができる実用的手法を提案した。更にシステム同定時とは異なった変動形態を持つ他の任意入力がこの複雑なシステムに印加されたときの出力応答分布をきめ細かく予測できる一手法を見出した。本手法を実音響システムに対する応答出力分布の予測問題に適用し、その有効性の一端を実際的にも確認した。

Most of actual environmental systems show a complicated fluctuation pattern of non-Gaussian type, owing to various kinds of factors. In the actual measurement, the fluctuation of random signal is usually contaminated by an external noise. Furthermore, it is very often that the reliable observation value can be obtained only within a definite fluctuating amplitude domain, because many of measuring equipments have their proper dynamic range and original random wave form is unreliable at the end of amplitude fluctuation. It becomes very important to establish a new signal detection method applicable to such an actual situation. This paper newly describes a dynamical state estimation algorithm for a successive observation contaminated by the external noise of an arbitrary distribution type, when the observation value is measured through a finite dynamic range of measurement. On the basis of the Bayes' theorem, this method is derived in the form of a wide sense digital filter, which is applicable to the non-Gaussian properties of the fluctuations, the actual observation in a finite amplitude domain and the existence of external noise. Differing from the well-known Kalman's filter and its improvement, the proposed state estimation method is newly derived especially by paying our attention to the statistical information on the observation value behind the saturation function instead of that on the resultant noisy observation. Finally, the proposed method is experimentally confirmed too by applying it to the actual problem for a reverberation time measurement from saturated noisy observations in room acoustics

This paper describes a new trial of dynamical parameter estimation for the actual room acoustic system, in a practical case when the input excitation is polluted by a background noise in contrast with the usual case when the output observation is polluted. The room acoustic system is first formulated as a discrete time model, by taking into consideration the original standpoint defining the system parameter and the existence of the background noise polluting the input excitation. Then, the recurrence estimation algorithm on a reverberation time of room is dynamically derived from Bayesian viewpoint (based on the statistical information of background noise and instantaneously observed data), which is applicable to the actual situation with the non-Gaussian type sound fluctuation, the non-linear observation, and the input background noise. Finally, the theoretical result is experimentally confirmed by applying it to the actual estimation problem of a reverberation time.

In the ultrasound diagnosis field, an analysis of speckle image texture in ultrasound B-scans is one of the important researches using stochastic signal processing method. In this paper, it is focused on finding out theoretically the probability density function of the speckle image texture for the magnitude of speckle image. First, the occurrence mechanism of speckle image texture is treated as a random walk problem in a multi-dimensional signal space based on Shannon's sampling theorem, by newly introducing a Hankel transformation type characteristic function. As a result, a unified probability density function expression has been explicitly proposed and it has been clarified that the present expression agrees with the well-known Rayleigh and Rician probability density functions as two special cases. Then, the legitimacy and the effectiveness of proposed stochastic analysis method has been experimentally confirmed by applying it to the speckle pattern of clinical B-scan image actually utilized for diagnostic purpose. © 1992, Acoustical Society of Japan. All rights reserved.

前報告では、刻々の残響過程においてエネルギーの統計的な揺らぎ形態が特に個々のモーメント情報に中心をおいて時間と共にいかに推移してゆくかを考察した。前報告とは異なり、本報告ではまず、計測の実際と現実の揺らぎの複雑さに対応できる離散型の一般化Fokker-Planck方程式を導出し、残響室における残響曲線の揺らぎ分布全体に関する過渡的推移表現をSabineの残響則を反映した逐次形式の形で新たに導出する。具体化にあたっては、エネルギー変量における物理的対策の足場と評価におけるdB観測に整合できるよう、この確率分布の推移法則における初期分布の枠組として、特に対数正規分布を初項に持つ一般的な展開分布表示を採用している。最後に、残響室内における実測例に適用して本手法の有効性を実験的にも検証している。

This paper discusses several types of the mutual correlation of information among stochastic fluctuations of the sound intensity at three observation points on the basis of a tri-variate joint probability distribution. First of all, the statistical Laguerre series expansion expression, taking the product of three Gamma distributions as its first term, and reflecting the linear and nonlinear correlations of fluctuations in each expansion coefficient, is introduced as the general framework of the tri-variate joint probability distribution. Needless to say, the Gamma distribution corresponds to a well-known probability distribution at a single observation point. Next, each expansion coefficient is derived in relation to the geometrical positions of the observation points, the frequency characteristics of the input, the time constant of the sound level meter, and so on. Finally, the validity of the proposed theory is experimentally confirmed by applying it to data actually observed at three points in a reverberation room.

任意周波数帯域幅の白色雑音入力を、拡散音場下の室に加えたとき、その不規則応答波が、任意K個の観測点において時間・空間的にどのような揺らぎ相関を持つか、その確率特性について理論的に考察する。具体的には、まずこれらの各種相関情報をすべて洩れなく導出できる任意多変量結合確率分布表示を一般表現の形で導出する。特に、2変量、3変量、4変量の場合について詳細に考察を行った。また、線形・非線形の各種相関情報を浮き彫りにするため、結合モーメント、条件付確率密度関数、条件付モーメントについての考察も行う。最後に、実際に残響室内において実験を行い、理論的に予測された曲線と実測値とを比較検討し、理論の有効性をも確認した。

This paper, which is dedicated to Dr. M. Jessel in celebration of his 70th birthday, gives an exact expression for the stochastic problem of N-dimensional random walks on the basis of information theory in close connection with room acoustics. The probability density function is derived for the sum of independent and isotropic random vectors in an N-dimensional signal space, when the magnitude is independent of the direction. First, a characteristics function of the Hankel transform type is newly introduced, because it is suitable for consideration of the probability problem of N-dimensional random walks, and can be used to derive an exact representation of the probability density function. Then, the probability density function is explicitly derived for the random fluctuation of a power scaled variable (or effective value) with a mean squaring function (for instance, the sound or vibration energy fluctuation observed via a sound level meter or sound vibration meter). Finally, the validity and effectiveness of the proposed theory is experimentally confirmed by the use of a digital simulation technique, and is discussed particularly in connection with room acoustics.

前報告では、メモリある音・振動環境システムの簡便な1変量出力応答分布がメモリ効果とゼロメモリ型非線形効果を機能的に分離し近似表現ではあるが両者を反映した統一的形態で導出された。特にエネルギー変量のみに着目した前報告とは異なり、本報告ではまず、エネルギースケールにおける物理変量に足場を置きながらもdBスケールでの観測データへも整合できる揺らぎ分布表現の一般的枠組みとして、対数正規分布を表現の基幹にとり、更に揺らぎの多様さへ互いに冗長度なきよう階層的に対処できる直交展開型分布表現を新たに導入した。本手法の有効性は、ロック音楽と交通騒音の侵入した室内音響における実問題へ適用して実験的にも確認された。

任意帯域幅の白色雑音を入力した拡散音場下の2観測点間で、音の強さに関する互いの揺らぎが持つ空間相関と各観測点で個々に示す揺らぎ分布の間の関連性についてまず理論的に考察する。両者を関連付けた揺らぎの結合分布が、入力の任意周波数帯域幅と計器の自乗機能や任意時定数の影響を具体的に反映させた2変量統計的Laguerre展開型の分布表示として導出される。この表示を基盤にして2観測点間の相関効果を考察するとき、低次から高次へ線形相関のべき級数の形で階層的に個々に調査する分析的立場と、条件付き確率密度の分布関数全体に着目する総合的立場の、対照的な二つの見地をとる。最後に、残響室内の実測データに本理論を適用してその有効性を実験的にも検証する。

Fluctuations at two observation points in a diffused sound field vary with correlations. In actual acoustic measurements, a sound level meter with a time constant is often used for a white noise input with a frequency bandwidth. Hence, fluctuations of the sound intensity must be considered first. Numerous studies have been reported on the probability density function and the spatial correlation in a diffuse sound field. How‐ever, the former is limited to a single variate distribution while the latter is restricted to the linear correlation of fluctuations. In this paper, the joint probability distribution of the fluctuations of the sound intensity is derived first so that various linear and nonlinear correlation effects between the fluctuations at two observation points are found in connection with the well‐known T‐type probability distribution at in dividual observation point. the resultant distribution expression is a two‐variate joint T distribution for which the arbitrary frequency bandwidth of the input and the effects of square function and arbitrary time constant of the measurement device are reflected structurally in each statistical parameter. Further, to distinguish all correlations between fluctuations at the two observation points A and B, the conditional probability density function on the fluctuation at the point A is derived in the case where a conditioned level is set at the point B. Finally, the present method is applied to the fluctuation data of sound measured in a reverberant room so that the actual usefulness is confirmed. Copyright © 1989 Wiley Periodicals, Inc., A Wiley Company

In the practical engineering field of noise control, it is as important as the sound source countermeasure to improve the sound propagation characteristics by newly setting a sound insulation system. On the other hand, the noise statistics like an Lx (x=5, 10, 50, 90, …) defined as a (100—x) percentage point of the sound level distribution are very important as well as the lower order energy moment statistics like an Leqin the actual noise evaluation and regulation problems. In this paper, two kinds of probabilistic evaluation methods for sound insulation systems are theoretically proposed from typically different points of view for the probability distribution of the transmitted sound intensity, when a general stationary random noise having an arbitrary distribution form and frequency characteristics is insulated by a wall. To evaluate its sound transmission coefficient, a somewhat modified statistical energy analysis method has been used. The validity of the theoretical results is experimentally confirmed by applying it to the actually observed data on the output response fluctuation of single and double walls type insulation systems inserted between two reverberation rooms. © 1986, Acoustical Society of Japan. All rights reserved.

The additive model with external fluctuation factors and the multiplicative model with internal fluctuation factors are well-known as two fundamental models describing the stationary and non-stationary random phenomena in the actual engineering field. An actual stochastic systems described by an additive model in a short time interval must be very often described in a long time interval by a mixed type stochastic model containing the fluctuation of multiplicative factor, because the internal parameter of the system changes with the passage of time. In this paper, first, by introducing a mixed type stochastic model for the actual random process, a unified expression is proposed for the probability distribution function of the above non-stationary composite wave measured by an arbitrary non-linear observation system. Next, by use of the above theory, two types of new methods identifying the probability distribution function of a specific factor embedded in the composite wave are derived in a general form of series expansion expression. Finally, by applying the above theoretical results to various types of L_<eq> evaluation problems of road traffic noises and industry noises based on the actual noise observations corrupted by the background noise, the validity of proposed evaluation methods is also experimentally confirmed.

In general, the descriptive approach on the stochastic evaluation is typically effective for the complicated situation of actual sound insulation systems with an actual random noise excitation which is impossible to evaluate by use of the well-known structual approach. In this paper, after once introducing descriptively a linear regression type system model between input and output, the system parameters have been estimated not in a sense of the usual least square error evaluation but in a sense of laying stress on the edge or the whole shape of probability distribution function. More concretely, this estimation method has been originally proposed by use of a stochastic approximation method for the purpose of extracting more effective information latent in the remainder fluctuation around the above linear regression, under a new error criterion based on equalizing a noise evaluation index L_aα and a Kullbacks information quantity for modelled and actual systems. Furthermore, in an actual case with an existence of background noise, a simplified trial of removing this background noise is also discussed. Finally, the effectiveness of the proposed evaluation methods has been experimentally confirmed too by applying it to the actually complicated sound environmental system.

Until now, the output probability distribution prediction for the sound insulation system was investigated by many researchers based on two contrastive structural and descriptive approaches especially from a methodological viewpoint. The descriptive method is certainly more suitable for the complicated stituation of actual sound insulation systems with an arbitrary distribution type random excitation. In this paper, especially by paying our attention to the effective information on the remainder fluctuation around the formally introduced linear regression, a simplified identification method for an arbitrary sound insulation system and then a simple prediction method for its output probability distribution have been proposed. More concretely, by introducing new types of linear and/or non-linear regression models between input and output fluctuations, their system parameters can be identified by use of the well-known least squares error method or its generalized error criterion. Furthermore, in an actual case with an existence of background noise, the effect and simple removal countermeasures of background noise are also discussed. The effectiveness of our identification and prediction methods is experimentally confirmed too by applying them to the actual living environment. © 1985, Acoustical Society of Japan. All rights reserved.

As is well-known, the wave form of random noise and vibration appearing in our actual enviroment shows usually the variety and the complexity in its fluctuation pattern. The statistical methods of analyzing and evaluating the above random wave form were studied by many researchers, from the viewpoint of signal analysis. In this paper, after first setting a generalized method of statistically evaluating the acuity of fluctuating random wave based on the information on each order of differntial type state variables, especially for the stational random wave of arbitarary distribution type, a new trial toward the statistical evaluation on the locations of level crossing, peak and trough has been concretely considered as the special cases, in close connection with the above differential type state variables. That is, in the proposed theory, the effect of usual linear correlations and non-linear correlations among two and/or many sampled points of random wave on the above probability distribution form of level crossing, peak and trough has been fully discussed under introduction of multivariate joint probability distribution. Finally, the practical effectiveness of the present theory has been experimentally confirmed too by applying it to the acrual road traffic noise wave obeserved ina suburb of a large city.

It is well-known that the level fluctuations appearing in the road traffic noise environment are brought on by various type causes and can be roughly classified into two great divisions on the road traffic flow pattern and the surrounding sound field. Accordingly, if the equivalent models for the above two divisions-traffic flow and its surrounding field are well established in a flexible form of reflecting the complex situation of actual road traffic noise field, it will be possible to predict precisely and/or to control effectively the road traffic noise. In this paper, from the above point of view, a stochastic model of road traffic noise with a generalized Poisson type flow is first introduced with many informations of actual situation. Next, an equivalent type sound propagation model is newly proposed in a form of mixing of two idealized sound propagation environments-a free sound field and a diffused sound field. Furthermore, a methodological trial to estimate the above equivalent sound propagation characteristics of the compound environment by measuring the actual road traffic noise data is derived from the system-theoretical point of view. In this case of estimation, the well-known stochastic approximation method is used in order to overcome the difficulty of non-Gaussian and non-linear characteristics existing in the actual environmental noise phenomena. Finally, the legitimacy of this estimation method is confirmed by applying it to the traffic noise data actually observed in a big city. PACS number: 43. 28. Fp, 43. 28. Hr, 43. 50. Lj, 43. 50. Vt, 43. 60. Cg. © 1983, Acoustical Society of Japan. All rights reserved.

スペクトル解析に関係する専門技術について、ハンドブックの一部を執筆した。内容は、脳波解析であり、「コンピュータの進歩と脳波解析」、「脳波の時間-周波数解析」、「独立成分分析」 に関し、それらの原理を説明するとともに、我々が行った脳波解析の結果も示した。

可聴音を用いて音源から物体までの距離を推定する手法について検討した。

感情音声の合成を目的として，声優が発声する自然音声の声質の特徴解析を行っている。今回は，音声信号のスペクトル傾斜に着目し，感情の種類との関係を調べた。その結果，「平常」に比べて「激怒」の方がスペクトル傾斜が大きいことがわかった。同様に，「喜び」におけるスペクトル傾斜も「平常」の場合より大きい。このことは，「激怒」および「喜び」の方が「平常」より高域が強調された声質に変化していることを意味している。２名の声優の音声５単語についてほぼ同様の結果が得られた。

音声に含まれる感情の種類・度合によって，音源に含まれる雑音のレベルがどのように変化するかを調べる研究の一環として，雑音量を定量化する指標である N/S 比について検討を行った。その中で，筆者らが提案した櫛形フィルタを用いた N/S 比の精度向上と計算の効率化を目的として，櫛の位置と幅を自動決定する手法を提案した。この手法では，残差パワーの周波数に関する二階微分値のピークを櫛の位置と幅の情報として用いている。この手法により，櫛形の自動調整が可能であるとの見通しがついた。

歌声には、人それぞれに声質がある。例えば、太い声、細い声、かすれ声、声域などが挙げられるが、このような個人の声質に合った歌曲を選曲するのはなかなか困難である。本研究では、歌声の声質の中でも特に声域に注目し、個人の声域により近い音域の歌曲の自動検索や指定曲を個人の声域の高さにより近くなるように移調するシステムを提案する。

音響分野に限らず信号の性質を調べるためにさまざまな方法が提案されており、なかでも時間-周波数分析法はしばしば用いられる。しかし、それらは一般に時間分解能と周波数分解能の間には不確定性の関係がある。近年、より精密な時間的変化，周波数的変化を同時に見るために時間-周波数でのパワー変化の分布（すなわち、正値時間-周波数分布）に着目する手法が提案されている。前報に引き続き本研究では、Copulaに基づく正値時間-周波数分布を導入し、音響信号の分析のために音声解析への応用を検討する。

対象物までの距離を推定するために超音波等がしばしば用いられ，その推定原理としては，送信パルスと対象物からの反射波との時間差が利用されている．しかし，この手法では対象物が数10cmに存在する状況では反射波が送信波に埋もれてしまい推定できなくなる．これに対してマイクロ波レーダの分野では，定在波を利用して近距離計測を行う手法が知られている．本研究では可聴音に着目し，スピーカから放射された音と対象物からの反射音の干渉によって生じる定在波を利用した距離の推定法を基礎から検討する．

計測自動制御学会関西支部からの依頼を受け講習会の講師を務めた。以下はその要旨である。 複数の独立信号が混合された観測信号から独立成分のみを取り出す独立成分分析 (Independent Component Analysis: ICA) が盛んに研究されている．これは単純な問題設定の割に解法がバラエティに富むためと，なにより潜在的な応用範囲が広いためと思われる．時間差のない信号の混合を Instantaneous mixture と呼び，時間差やシステムの影響を受けた場合を Convolutive mixture と呼んで区別している．このような状況において信号を分離することをブラインド分離(Blind Source Separation: BSS)問題と呼び，とくに Convolutive mixture の場合に信号源まで復元することをBlind Source Deconvolution問題と呼んでいる．ICAは原理的にはどちらの混合に対しても用いることができる． ICA はさまざまな分野で用いられるが，とくに音響信号については当初から特にカクテルパーティ効果などと関連して，音声分離のシミュレーシ

混合に時間差などの影響があるブラインド分離問題に対しては、周波数領域における複素ICA(独立成分分析) がよく用いられ、著者らも複素ICAの一解法を提案している。 本研究では、複素 ICA に基づいて時間差混合信号を分離する際得られる分離行列から遅延時間・振幅比の推定を行う。これを用いて混合信号の逆フィルタを構成し、実信号として帯域歪みのない分離・再生を目指す。

混合信号のブラインド分離については多くの研究が報告されており，著者らも以前に瞬時混合に対して Hermite モーメントと回転変換により，畳み込み混合に対して複素Hermiteモーメントとユニタリ変換(SU(2))により取り扱った． 本報告では，3つの複素信号が混合された場合に拡張する．具体的には，規格直交化された観測信号に対し，複素Hermite モーメントに基づく評価関数を最大化する3次元のユニタリ行列(SU(3))を推定する．最後に本手法の正当性をシミュレーションにより検証する．

音響分野に限らず信号の性質を調べるためにさまざまな方法が提案されている。なかでも時間-周波数分析法はしばしば用いられるが、一般に時間分解能と周波数分解能の間には不確定性の関係がある。近年、より精密な時間的変化，周波数的変化を同時に見るために時間-周波数でのパワー変化の分布（すなわち、正値時間-周波数分布）に着目する手法が提案されている。 本研究では、正値時間-周波数分布による音響信号の分析のために、Copulaに基づく正値時間-周波数分布の具体的な算出法を検討し、テンプレートとしてスペクトログラムを採用し、楽音への適用を行う。

混合信号のブラインド分離については多くの研究が報告されており，著者らも以前に複数の独立信号の同時混合を Hermite モーメントと回転変換により取り扱った．また，混合に時間差や残響などの影響がある場合には，混合信号を複素狭帯域化した後，分離する周波数（複素）領域での ICA も提案している．2信号に対しては複素HermiteモーメントとUnitary変換(SU(2))を利用するが，本報告では 3信号が畳み込み混合された場合に拡張する．具体的には，規格直交化された観測信号に対し，複素Hermite モーメントに基づく評価関数を最大化する3次元のUnitary行列(SU(3))を推定する．最後に本手法の正当性を検証するため，計算機シミュレーションを行う．

音響信号の性質を調べるためにさまざまな方法が提案されている。なかでも信号の時間的特徴と周波数領域での特徴を同時に調べることのできる時間-周波数分析法は強力なツールとしてしばしば用いられる。時間-周波数分析法には、スペクトログラム（短時間フーリエ変換）、Wigner分布、Choi-Williams分布などのいくつかの手法が知られている。一般に、時間-周波数分析ではエネルギー分布を用いるが、正値分布としての条件をすべては満足していない。 本報では、周辺分布などの条件を満足するCopulaに基づく正値時間-周波数分布に着目する。これにより、たとえばスペクトログラムなどに比べ、時間と周波数両方において分解能の向上が期待できる。最終的な目標を正値時間-周波数分布による音響信号の分析と定め、今回はCopulaに基づく正値時間-周波数分布の具体的な算出法を検討する。最後にテンプレートとしてスペクトログラムを採用し、簡単なシミュレーションや楽音への

電磁波の分野では、不規則に揺らいでいる媒質中を波が伝わるとき、波が小さな領域に閉じ込められる局在現象が知られている。よって、ランダム媒質あるいはランダムな装荷をもつ音場でも指数関数的な音の減衰があり、それを騒音抑圧に利用可能と思われる。 ランダム媒質による減衰効果を考察した既発表に引き続き、本研究では1次元音場の等価回路表現を用いて、ランダム装荷をもつダクトの減衰特性を検討し、シミュレーションにより正当性を検証する。

複数の信号が混合された観測信号から源信号を分離する問題をブラインド分離という。その解法の一つに源信号の統計的独立性に基づく独立成分分析(ICA)がある。本研究では、著者等の提案している Hermte モーメントに基づくICA 手法を、多チャンネルの脳波(EEG)データの分離に適用する。本手法により、ノイズ成分(アーチファクト)を取り除けることが分かった。 (英文)

源信号の統計的独立性に基づいて混合信号をブラインド的に分離する独立成分分析(ICA)が盛んに研究されている。著者等も、Hermite モーメントに基づく評価関数と回転変換により独自のICA アプローチを提案している。本研究では、対象信号以外の成分が存在する場合、評価関数にどのような影響を及ぼし、その結果、分離性能がどの程度劣化するかを理論的に考察した。シミュレーション実験でも良好な結果が得られている。

甲南大学の ORC(オープン・リサーチ・センター)の客員特別研究員として講演を依頼され、著者らの手法を中心に，ICA(独立成分分析) の基礎理論とその信号処理への応用について解説した．また，音声・画像でのシミュレーション結果や実際の生体信号への適用結果の一例も示した．

電磁波の分野では、不規則に揺らいでいる媒質中を波が伝わるとき、波が遠くまで伝わらず小さな領域に閉じ込められる現象が知られている(局在現象)。音場においても同様に指数関数的な減衰が期待でき、騒音抑圧に利用可能と思われる。本研究では既発表に引き続き、1次元音場の等価回路表現を用いて、ランダム性をもつダクトの減衰特性を検討し、シミュレーションにより正当性を検証する。

2信号の場合について複素Hermiteモーメントとユニタリ変換(SU(2))に基づく複素 ICA をすでに報告している。本報告では、3つの複素信号が混合された場合に拡張する。具体的には、規格直交化された観測信号に対し、複素Hermite モーメントに基づく評価関数を最大化する3次元のユニタリ行列(SU(3))を推定する。

平成１６年電気関係学会関西支部連合大会の信号処理分野のシンポジウム「信号処理の現状と未来」に招かれ、独立成分分析(ICA) の原理と音響信号処理への応用について講演した。さらに、音源方位推定への本手法の適用例も示した。

電磁波が、不規則に揺らいでいる媒質があると局在現象が起こる。本研究では1次元音場の等価回路表現を用い、媒質がランダムな特性を示す場合、音でも同様の局在化が起こることを示し、減衰特性についてシミュレーションを行い、その正当性を検証する。

１次元ダクト内の音の振る舞いは電気工学の等価回路を用いて表すことができる。本研究では、マイクロホン２本の観測信号を用いて騒音を打ち消すために２段のフィルタを導入した。さらに帯域信号を用いたシミュレーションによりその正当性を検証した。

騒音を逆位相の音で打ち消す能動騒音制御(ANC)について、特に１次元ダクトに着目して、回路理論に基づき新たな制御理論を提案し、純音に関するシミュレーションによりその正当性を検証した。

近年盛んに研究されている独立成分分析(ICA)では、対象外成分が存在すると分離性能は劣化する。本研究では、著者らがすでに提案しているHermiteモーメントと回転変換に基づくICA 手法について，対象外成分によりどのように推定精度が劣化するか検討し，シミュレーションを通じて確認する．

分布定数系の等価回路により1 次元音場を書き直すと、主・副音源を用いた音場の制御が原理的に可能となる。これによると騒音制御用のフィルタ設計も容易である。本研究では、とくに1 次元ダクトを具体例とするシミュレーションを報告するが、結果は良好であった。

時間差混合信号に対する複素ブラインド分離の分離行列から遅延時間・振幅比の推定を行い、音源位置・方位を推定する手法を提案する。さらに推定パラメータを用いて混合信号の逆フィルタを構成することにより、帯域歪みのない実信号としての分離・再生を行う。

複素ICA（Independent Component Analysis）に基づいて時間差混合信号を分離する際得られる分離行列から遅延時間・振幅比の推定が行える。これにより音源位置の推定が原理的に可能となる。本研究では、音声によるシミュレーションを通じて理論の正当性を検証する。

すでに1 次元ダクトの伝送線路モデルを基本にして1 次元ダクトの能動騒音制御（Active Noise Control：ANC）を考察している。本研究では、既発表の理論に基づいて行ったシミュレーションを中心に報告した。結果は良好であり、理論の正当性の一部が示せた。

様々な観点から研究がなされている能動騒音制御（Active Noise Control：ANC）について、とくに1 次元音場に対し等価回路に基づき考察した。本手法は、既存の手法に比べ、ANC の原理ならびに、制御回路の周波数特性が単純で把握しやすいという特長がある。

既発表の1次元ダクトの等価回路に基づくANCは、既存の手法に比べ、ANCの原理ならびに、制御回路の周波数伝達特性が単純で把握しやすく、フィルタの構成も容易である。本報告では、簡単なシミュレーションを通じて理論の検証を行ったので報告する。

音源位置あるいは方向の推定のために、複素ICAに基づいて時間差混合信号の分離行列から遅延時間・振幅比の推定を行う。さらに、提案した逆フィルタによって、実際の音声信号で帯域歪みのない分離・再生ができることを、シミュレーションを通じて示す。

時間差混合信号に対し、複素ICAによる分離行列から遅延時間・振幅比の推定を行えば、分離と同時に音源位置あるいは方向の推定が原理的に可能である。さらに推定パラメータを用いた逆フィルタにより、帯域歪みのない分離や再生ができることを確かめた。

本報告では、前報告に引き続き、中型の防風スクリーンを装着した場合、また、風車発電機の騒音計測に用いられる計測システムを用いた場合の低周波雑音成分が、それぞれマイクロホン近傍の風速情報を用いて推定可能かどうかを実験的に検討している。

前報に引き続き、観測信号から風雑音を除去する手法を提案する。とくに実用的な観点から風速と風雑音の関係は線形モデルで記述し、その関係の時間変化も考慮する。さらに実際の風雑音混入下における音響信号検出の問題に本手法を適用し、その有効性を議論する。

The purpose of this research is to realize a distaince measurement system for detecting the distance to a human being using audible sound for devices such as nursing care and welfare robots that require a wide range of distance detection from near to far. However, the conventional method has a problem that the measurement accuracy is degraded by the influence of the measurement system between the loudspeaker and the microphone and the observation noise in the real environment. In this study, (1) a theory for the measurement is developed under high noise conditions, which is not possible with the conventional phase-interference-based acoustic distance measurement method, (2) a theory for eliminating the influence of the measurement system between the loudspeaker and the microphone is developed, and (3) the acoustic distance measurement method to a specific object is investigated. The results suggest the effectiveness of the proposed method.

(1) We introduced L and U filters having not been well-known as morphological filters and the digital pulse transform (DPT) constructed of L and U filters. (2) We proposed a new method for detecting randomly generated signals buried in noise, in particular, a new method to detect saccades in human eye movement data. We attained error-free detection of the saccades by this method which has not been achieved by traditional linear filters. This method can be widely applied to detection problems in biomedical environmental data processing. (3) Agaist the commomly accepted theory that median filtering outperforms traditional linear filtering in preserving signal edges while reducing noise, we theoretically proved that moving average filter is a better smoother preserving signal edges than the median filter under a practical wide range condition.

The purpose of this study is to realize the distance measuring system for detecting the distance by using the audible sound, especially in a close range (e.g., where a nursing-care robot care for human). (1) Based on the previously proposed acoustic distance measurement method (ADM) using a standing wave (or phaseinterference), we improved the original ADM method, and we considered the properties and potentials of the improved ADM method. (2) We considered ADM method to measure the distance shorter than the minimum measurable distance which is defined by the bandwidth of transmitted signal. Furthermore, (3) we considered the principle method for the moving target though the original ADM method is not applicable to the moving target. Thus, it becomes possible to measure both the velocity and distance for the moving target. This implies that the distance between microphone and target is measurable eve in a case when both microphone and target are moving.

The purpose of this study is to realize a rear-sonar of automobile for detecting obstacles(or targets) behind the automobile, using the exhaust sound of the automobile emitted from the automobile muffler. (1) We considered the fundamental properties and potentials of the distance estimation method based on the phase interference of audible sound. (2) We developed several methods, so as to reduce the error due to geometrical positions of the loudspeaker, target and microphone and the error due to the effect of the observation noise and measurement system. Furthermore, (3) we proposed a distance measurement method to measure the distance shorter than the minimum measurable distance.

(1) We proposed a new mutual information criterion for deciding an optimal mixture distribution and an optimal threshold. (2) We proposed the usage of Renyi's alpha-entropy as a measure of width of marginal distribution and obtained very intuitive new and simple ICA methods. (3) We proposed an adaptive method for smoothing the periodogram for positive time-frequency representation. For impulse train time-frequency analysis, we proposed an inverse domain demodulation method of IPFM and an objective evaluation method for demodulators. Further, we proposed distance estimation method exploiting time-frequency feature of reflected signal from a moving object.

It is known that a wave cannot propagate long distance in random media and is confined in a small region when the field is excited. In physics it is called the "localization", the phenomenon which is closely related to the cut-off (non-propagating) state of waves in a certain broad frequency band. It is expected that this property can be utilized as a muffler to reduce the sound noise because the sound propagating in random media or random loadings would exhibit strong exponential decay along distance. On the other hand, a one-dimensional acoustic duct can be expressed by a transmission line model commonly used in the study of microwave waveguide. In this research, I focus on the sound decaying property of one-dimensional duct (random duct) and demonstrate the validity of the proposed theory through a computer simulation. The results I obtained in 2005 and 2006 are listed below.[2005 year] : As the first step of research, I expressed the sound field in duct by a transmission line model, on which I theoretically analyzed the ordinary one-dimensional duct and carried out computer simulation. Based on the circuit representation, I theoretically proposed the sound reduction property in a case when there exist random media in duct. To confirm the validity of the analysis, I performed the computer simulation and showed the existence of the strong exponential decay. These results have been published in a scientific journal and presented in domestic conference.[2006 year] : Following to the fundamental consideration on the sound reduction problem with randomness in 2005, I theoretically proposed the sound reduction property in a case when there exist random loadings in duct and the extensive simulation makes it clear that the proposed method also enables us to cause the strong exponential decay. These results have been presented in international conferences.

Sound source localization problem has been important in various actual fields of acoustics and many approaches have been developed e.g., MUSIC, etc. Most of them utilize only the lower order statistics of observations such as a covariance matrix and the orthogonality (or uncorrelation) between the objective signal and noise. Recently , Independent Component Analysis (ICA) becomes popular to solve a blind signal separation problem where independent sources are mixed and then measured by multiple sensors. The ICA of complex signals has been also proposed for a case when observations have time differences between source signals or are affected by system (room etc.).In this research, some trials of estimating the sound source positions or directions are proposed from various viewpoints. In particular, most of them are based on the statistical independency between source signals or between the source signal and an additional noise. The results we obtained in 2001 and 2002 are listed below.[2001 year]: As the first step of research, the correlation method is introduced to calculate the delay time between observations at each microphone and then to estimate the sound direction. In the second approach, MUSIC method and Kalman filter are employed, respectively, to estimate the direction of source and to detect the amplitude information for sound source localization.The third method is a trial of estimating the time delays or the distances between receivers and sound sources based on the complex ICA, especially for the mixed observations with time delays. Further, we can easily construct an inverse filter to separate the (over-all) real mixed signals using the parameters estimated by ICA, while the usual complex ICA required synthesizing all frequency components. Finally, through fundamental simulation, we demonstrate the high-quality blind separation as well as the validity for the estimation of the source parameters.[2002 year]: Following to the fundamental consideration on the sound source localization problem in 2001, the extensive simulation makes it clear that the proposed method also enables us to find the directions of arrival. These results have been presented in domestic or international conferences.

The main objective of this research is to make a plan and investigation for a joint research project on "Agricultural Resource Management taking into account Eco-system and Environment Problems"with IIASA (International Institute for Applied Systems Analysis) and Prof. R.H.Richardson of Texas University. To this end, 1. We co-organized a workshop on "Agricultural Resource Management taking into account Environment Problems" with the Society of Animal Production Systems, and observed Mt. Sanbe national park in which grass ground was recovered by pasturage. 2. We observed Saito Farm and others which succeeded in creating excellent environment with beautiful view by reclamation by pasturaged cattles, and co-organized a symposium on "Agriculture in Harmonious with Natural Eco-systems" with the Society of Animal Production Systems, and Open Network for Nature Conservation, In the symposium, we discussed and exchanged ideas on the basis of lectures i) Holistic Management in Agriculture in Harmonious with Eco-systems by Prof. R.H.Richardson of Texas University, and ii) Land Use Problems taking into account Earth Scale Environment by Dr. G.Fischer of IIASA. 3. We investigated the activities of Lake Biwa Research Institute, and had a meeting with a fisherman in Biwa Lake and a large scale farmer to discuss fishing and farming from the viewpoint of environmental management. Through the above activities, we clarified the theme and direction of our planning international joint research in the future.

本研究では、我々の生活と切り放すことができない音環境システムに特に着目し、その信号処理を目指して、多変量解析の分野で公知の主成分分析法と因子分析法の拡張を試みた。まず、特に音環境における確率評価量(例えば、Lx、Leq)間での双方向変換関係を見いだす目的で、公知の主成分分析法を理論的に拡張した。具体的には、線形関係および自乗誤差評価(すなわち、線形相関を利用)のみに基づく従来の手法とは異なり、非線形モデルの導入や、高次相関情報の誤差評価への利用などを行なった。さらに、公知の回帰分析法と対比させながら提案手法を実測データに適用し、良好な結果を得た。この成分分析の拡張手法には次のような特長がある。すなわち、1)実現象ごもつ複雑さや各変数間の非線形性に対応できる、2)多変数間の線形相関情報のみでなく非線形相関をも利用できる、3)従来の主成分分析法をスペシャルケースで含んでいる、4)2変数のみでなく、3変数以上の場合のもそのまま本手法が拡張できる、などである。ついで、音環境における複雑な多数遮音システムを、暗騒音に埋もれた出力観測のみから同時に同定したり、その出力応答を(騒音評価量とも関連し)揺らぎ分布全体において予測する目的で、特に実用的な立場から因子分析法の考え方を拡張した。具体的には、共通因子と独自因子に実体的メカニズムをまず反映させて、それぞれ騒音入力インテンシティ、各観測点での暗騒音インテンシティとして捉え、インテンシティスケールでの線形モデルに基づきシステムパラメータとして因子負荷量を推定した。この結果を用いて、暗騒音の影響がない場合、すなわち入力騒音のみに対する出力騒音の分布予測を行うことができる。さらに、本手法を実際の音環境データへ適用することによりその有効性を実験的にも確認できた。この因子分析の拡張手法は次のような特長を持っている。すなわち、1)複数システムを同時に扱える、2)入力および暗騒音が未知でも適用できる、3)計測において入出力間の同期をとる必要がない、などである。

本研究では、もともとの変動が有限な範囲内に留まっていたり、(飽和型非線形系の)計測器のダイナミック・レンジなどの存在により有限な範囲内の値を示す実際的な場合において、非定常入力を伴う系の応答解析を最終目標としている。今回は研究の初期的段階にあることから、特に飽和型非線形系における非定常変動観測時の雑音対策を、システムの物理メカニズムと直結するパワースケールとの関連で考究した。すなわち、有限レベル変動範囲のダイナミック・レンジをもつ観測データを用いて、任意分布型の外来雑音に汚された未知非定常信号(特に、パワースケールのような正の物理量)を、動的に推定してゆく推定アルゴリズムをベイズ定理に基づき開発した。具体的には、飽和の影響を受ける前の任意変動の観測値と任意非ガウス型変動を示す未知信号間の線形・非線形の各種相情報を階層的に反映した新たな信号復元法を、広義ディジタルフィルタの形で見い出した。更に本研究で得られた理論的結果を、シミュレーションデータや残響室内における暗騒音混入下の実音響データに適用し、その有効性を検証した。本研究で得られた理論の特長を列挙すると以下のとおりである。1)本手法は、外来雑音の混入とダイナミックレンジの存在に整合している。2)実システムが本質的にもつ非ガウス性、非線形性に対応できる。3)推定アルゴリズムが実用的である。すなわち、観測レンジ内では従来のベイズフィルタを形式的に採用し、観測レンジの上限、下限では確率密度の集中を簡易的に考慮している。4)スペシャルケースとして、ダイナミック・レンジが十分広い場合には、従来のベイズフィルタを理論的に包含している。本研究をもとに、今後、非定常な確率現象と計測における有限性を伴うあらゆる実分野への適用とその成果が期待できる(たとえば、機械振動、地盤振動、道路交通騒音などにおける非定常揺らぎの評価や解析など)。