Home HomeDavid E. Newland, University of Cambridge
Harmonic wavelets have simple formulations in the frequency domain and they have proved a good basis for the time-frequency mapping of transient signals. Moreover their computational algorithm allows bandwidth to be chosen arbitrarily so that they offer a variable Q transform, where Q is the ratio of centre frequency to bandwidth. In contrast, the short-time Fourier transform and the Wigner-Ville frequency decomposition method are constant bandwidth transforms, so that Q increases as frequency rises. Although properties of wavelet orthogonality may be used to permit easy retrieval of the input signal, to achieve a high-definition time-frequency map more data is required than that obtained from a single decomposition of the input signal. This is achieved by repeating the frequency decomposition for different, overlapping bandwidths in order to increase the number of points that can be plotted. Because bandwidth can be chosen arbitrarily, a frequency zoom feature can be incorporated into the harmonic wavelet transform algorithm. Also, because harmonic wavelets are complex, with real and imaginary parts, phase variations can be studied. Local changes in the spectral composition of a signal can be recognised, using either wavelet amplitude or phase as the discriminator. Examples of frequency zoom and of segmentation by amplitude and phase are given below. They demonstrate that the complex harmonic wavelet transform offers a computationally-efficient method of signal decomposition. Its principal advantage over the STFT is its variable Q property which becomes important when large amounts of data have to be processed.
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Mitsuo Ohta, Kinki University (Japan)
Akira Ikuta, Hiroshima Women's University (Japan)
The acoustic phenomenon in the actual living sound environmental system involves a variety of compound problems- Not only the natural, social but also the psychological factors make them further complicated and diversified. The frequency range of fluctuating sound pressure with no D.C. component is so wide that it originally can have a variety of fluctuation patterns with non-stationary and non-Gaussian properties. This presentation gives a basic and essential idea of our works on the stochastic signal information processing for acoustic environment, that is based not only on the lower order linear correlation but also on various types of the higher order nonlinear correlations. The importance of employing these higher order nonlinear correlations is discussed through the concrete establishment of wide sense digital filters. These digital filters are fundamentally based on the hierarchical expansion expression of Bayes theorem by using the orthogonal polynomials. The proposed digital filters can estimate any kinds of statistics of arbitrary functional type of a state variable including the lower order statistics connected with the material-side countermeasures (from a bottom-up way viewpoint) and the higher order statistics connected with the human-side evaluation indices (from a top-down way viewpoint). The validity amd the effectiveness of these filters are experimentally confirmed by applying them to the real acoustic environmental problems.
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Alexandros Soumelidis, Hungarian Academy of Science (Hungary)
Jozsef Bokor, Hungarian Academy of Science (Hungary)
Istvan Nagy, Hungarian Academy of Science (Hungary)
Nowadays the joint time-frequency analysis and wavelet techniques have stepped out from the academic research sites and spread out to several industrial applications. The static nature of the conventional spectral techniques used in the analysis of vibrating structures means considerable limitation in certain type of systems and problems arisen on them. Fast changes in the vibrating structures and the presence of transient effects need advanced methods for a compromise-free analysis. The startup or shutdown processes of large rotational machines are typical examples. Continuous monitoring and failure detection of the startup process of large rotating machines (e.g. turbine - turbo generator machine group in conventional or nuclear power plants) is a significant means to avoid serious damages or accidents, hence to save costs of operation and maintenance. The application of wavelets (1) in analyzing the transient vibration process by preserving the harmonic behavior of vibrations in the joint time-frequency methods, e.g. the short-time Fourier transform, the Gabor transform, the Wigner-Ville transform, and their generalizations and completions (2). A new, novel approach with wavelets stems from the approximation properties of these type constructs. The approximations of functions (i.e. signals) belonging L2, Linf, H2, Hinf, as well as the unit disc form nowadays a rapidly evolving field with applications in the identification and detection (3,4). This paper is devoted to investigation how can a priori information (derived from the physical and technological knowledge) be used in wavelet approximations with the purpose of efficient detection specific phenomena in the vibration signals. The appropriate selection of the mother wavelet is crucial in this action, which - sorry to say - cannot be done with full freedom; a significant argument is computability , i.e. the existence of realizable algorithm. The example used to represent methods is based upon real records of startup processes on turbo-generator machine groups of the Nuclear Power Plant Paks (Hungary).
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Michiko Kazama, Acoustic Consultant (Japan)
Takahiro Ohnishi, Kogakuin University (Japan)
Mikio Tohyama, Kogakuin University (Japan)
This article describes a method for reducing the noise of noisy speech signals based on a sinusoidal wave model (T. Quatieri, and R. Mcaulay IEEE ASSP-34,(6) 1986 pp1449-1464). The authors reconfirm that intelligible speech signals can be synthesized, even using only a few (say 5) sinusoidal waves, and propose a spectrum peak-picking method for noise reduction. The sinusoidal components necessary for speech signal representation are extracted from noisy speech using the short-time Fourier transform (STFT) and the noise-reduced speech signals are synthesized. This method increases the signal to noise ratio (S/N) of recovered speech signals, but the tonal quality is not completely acceptable. The authors also investigate the estimation of speech signals under noisy conditions using a harmonic sinusoidal model. They propose using a multi-windowed STFT (MW- STFT) to estimate the fundamental frequency of a speech and its harmonics sieving. Speech quality and S/N enhancement using MW-STFT based on the harmonic sinusoidal model are also demonstrated.
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Hitoshi Ogawa, Hiroshima National College of Maritime Technology (Japan)
Mitsuo Ohta, Kinki University (Japan)
In this paper, some generalized regression analysis method considering not only linear correlation but also higher order nonlinear correlation information is especially proposed in order to find mutual relationship minutely between sound and electromagnetic waves leaked from an electronic information equipment, Concretely, a hierarchical extended regression analysis method reflecting various type correlation information is theoretically derived by introducing an expression of multi-variate probability distribution in an orthonormal expansion series form. The effectiveness of the proposed theory is experimentally confirmed too by applying it to the observed data leaked from VDT in the actual working environment,
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Naomitsu Takaki, Hiroshima-Denki Institute of Technology (Japan)
Mitsuo Ohta, Kinki University (Japan)
In the actual situation of measuring an environmental noise, it is very often that only the resultant phenomenon fluctuation contaminated by an additional noise of arbitrary distribution type can be observed. Therefore, for the purpose of predicting the output response probability of acoustic system with an arbitrary stochastic input in the presence of the additional noise, it is necessary to find some new stochastic signal processing method reflecting the effect of the above additional noise fluctuation. In this paper, first, a relationship between the system output excited by a specific stochastic input of reference type and an arbitrary random input without the additional noise for an arbitrary acoustic systems is introduced in the form on an intensity scale. Next, a relationship between the system output excited by an arbitrary stochastic input in the absence and that in the presence of the additional noise is also introduced in the form on an intensity scale. Then, based on these relationships, a new prediction method of the system output for the arbitrary acoustic systems with the additional noise is proposed especially by use of the observed data excited by the specific stochastic input of reference type with the additional noise. Finally, the effectiveness of the proposed method is confirmed experimentally too by applying it to the actual type sound wall systems.
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Noboru Nakasako, Kinki University (Japan)
Yasuo Mitani, Fukuyama University (Japan)
Mitsuo Ohta, Kinki University (Japan)
An actual sound environment often shows complicated fluctuation patterns apart from a usual Gaussian type. Various evaluation procedures for the sound environment were methodologically proposed, owing to the variety of phenomena and the complexity of human response to them. It is very difficult to evaluate precisely the proper characteristics of complicated systems only from a physical viewpoint based on the structural mechanism. In such situation, a regression analysis function is usually employed between the input and the output fluctuations especially under the assumption of Gaussian property for the input-output fluctuations and/or the usual least squares error criterion. Furthermore, the extended regression analysis method which we previously reported was necessarily reduced in a complicated mathematical form, though it could utilize the lower and higher order correlations on the basis of Bayes' theorem. This paper describes a regression analysis matched to the prediction of the output response probability for complicated sound environmental systems by introducing a hierarchical neural network with statistical structure. Then, based on the estimated result, the output probability can be easily predicted for the same system with arbitrary input signal. Finally, the effectiveness of the present method is experimentally confirmed by applying it to the actually observed data.
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Yasuo Mitani, Fukuyama University (Japan)
Mitsuo Ohta, Kinki University (Japan)
In an actual measurement of random fluctuations, e.g., sound, light and electromagnetic wave fluctuations, the measured data are very often processed in a level-quantized form at discrete time intervals. This is because various statistical evaluations and extraction of the lower and/or higher order statistical information (e.g., mean, variance, median, higher order moments, 90% range, etc., sometimes a quasi-peak value) become easier by use of a digital computer. In this paper, a unified explicit expression for the probability function with level-quantized random variables for an arbitrary random fluctuation is theoretically derived in the general form of a statistical orthogonal expansion series. Next, based on this general theory, a new procedure for estimating the precise level distribution on the basis of information on the moment statistics calculated especially from roughly quantized level data is proposed. Finally, the effectiveness of the proposed theoretical method is experimentally confirmed by applying it to the actual data measured in front of VDT under the working situation.
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Yoshiaki Takakuwa, Hiroshima-Denki Institute of Technology (Japan)
Mitsuo Ohta, Kinki University (Japan)
Masafumi Nishimura, Hiroshima - Denki Institute of Technology (Japan)
Hideo Minamihara, Okayama University of Science (Japan)
This paper describes a new method estimating an objective low-frequency acoustic sound contaminated with wind noise in the outdoor measurement. It is a dynamic estimation technique employing a reference band pressure level (BPL) of a particular frequency range of the observation as the basis of the wind noise estimation. First, a conditional probability distribution function (c.d.f) of the wind noise on knowing the reference BPL is shown. Next, a dynamic state estimation technique based on Bayes' filter is proposed by using the consecutively renewed parameters of c.d.f. of the wind noise as a trial. This method is fairly different from previously proposed state estimation method based on the use of the information on the wind speed observed in the vicinity of the microphone. Because the proposed method becomes comparatively complicated for the practical use, more simplified stochastic estimation methods of the objective sound are also proposed. Finally, the effectiveness of the proposed method is experimentally discussed by employing these simplified methods in this study, especially from the practical view point.
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Hideo Minamihara, Okayama University of Science (Japan)
Mitsuo Ohta, Kinki University (Japan)
Naomitsu Takaki, Hiroshima-Denki Institute of Technology (Japan)
Masafumi Nishimura, Hiroshima - Denki Institute of Technology (Japan)
In this paper, an estimation method of the original stochastic information in random noise signals of which the amplitude fluctuation is limited by upper and/or lover levels is proposed for the generalized case of non-Gaussiam random signals. First, an explicit expression of the probability density function for the random signal with amplitude limitations is introduced by using a combination of the well known statistical Hermite orthonormal expansion form and the Diracs delta function. The original stochastic information is closely related to all of expansion coefficients in the probability density expression, and accordingly can be evaluated through the coefficients. That is, by use of this expression, the first, second, ..., nth order moments can be expressed by using the expansion coefficients, the definite integration values of the standard Gaussian distribution and the levels of amplitude limitations. Thus, the expansion coefficients directly connected with the original case with no amplitude limitations can be evaluated by comparing experimental values of the statistical momenta based on the limited observed data with the theoretically calculated moments. The stochastic information for the case with no effect of the amplitude limitation can be estimated through the expansion coefficients. Finally, the effectiveness of the proposed method is confirmed experimentally by means of the digital simulation technique, and by applying it to actual noise data.
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Shoji Kodani, Industrial Research Institute (Japan)
Mitsuo Ohta, Kinki University (Japan)
In this paper, after introducing a fundamental theory for the acuity of arbitrary fluctuating random waves, and some new trials of evaluating statistically and hierarchically the random noise and vibration wave forms of arbitrary non-Gaussian type distribution are proposed, especially by employing the multivariate joint probability density function of series expansion type. First, the counting number that two wave curves contact each other in lower and/or higher order differential forms is estimated and explicit expression of probability distribution on the instantaneous amplitude, velocity and successive higher order differential type physical quantities of the actual random waves can be concretely derived. Especially for the stationary random wave of arbitrary distribution type, a trial toward the statistical evaluation on the locations of level crossing is considered in more detail as a special case, in close connection with the above differential type physical state variables. Finally, the effectiveness of the proposed method has been experimentally confirmed by applying it to complicated fluctuation wave forms of the actual road traffic noise wave.
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Akira Ikuta, Hiroshima Women's University (Japan)
Mitsuo Ohta, Kinki University (Japan)
In the actual sound environment, a specific signal shows various types of probability distribution forms apart from a standard Gaussian distribution due to the diversified causes of fluctuation. Furthermore, the actually observed data often contain some fuzziness due to the existence of confidence limitation in measuring instruments, permissible error in experimental data and a level quantized error in digital observation. In this study, a new estimation theory for a specific signal, based on the observed data containing the fuzziness and the effects of non-Gaussian property is proposed from the static and dynamic viewpoints. More specifically, by applying fuzzy probability to a probability expression with an infinite expansion series form, a static method to estimate the probability density function of the specific signal based on the fuzzy observation data is first proposed. Next, a dynamical method of estimating only a specific signal state embedded in the additional noise (ie background noise) with random fluctuation of non-Gaussian type is theoretically derived especially in a flexible form applicable to these fuzzy observation data. Finally, the varidity and the effectiveness of the proposed method are confirmed experimentally by applying it to the actual road traffic noise data.
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Seijiro Hiromitsu, Hiroshima Shudo University (Japan)
Mitsuo Ohta, Kinki University (Japan)
A statistical treatment for the output probability is proposed by introducing a statistical Lagrange series expansion method, where a general random process of arbitrary distribution type is passed through a time-variant linear environmental vibratory system with an arbitrary non-linear feedback element. A typical example is seen in an environmental vibratory system described by Duffing's non-linear differential equation. In order to find the effect of non-linear feedback element reflecting an environmental criterion, the explicit expression of the output probability distribution is derived in the general form of non-orthogonal expansion series, reflecting the effects of the forward linear element of the system into the first term. In view of the arbitrariness of the input characteristics, non-linear elements and fluctuation forms of system parameters, the validity of theoretical expression is experimentally confirmed by the method of digital simulation.
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Yoshifumi Fujita, Onomichi Junior College (Japan)
Mitsuo Ohta, Kinki University (Japan)
In general, it is difficult to find some large scale model only from a bottom up way viewpoint for complicated sound insultion systems like non-parallel double wall or sound-bridge type double wall. Furthermore, in the actual environment, the input fluctuates non-stationarily and the output is observed under contamination of the background noise. In this paper, for the above complicated systems with non-stationary random input, a new evaluation method is proposed by newly introducing a multiplicative-additive system model on an intensiy scale. Owing to non-Gaussian property of input, output signals and background noise, the usual identification method such as least-squares error method is not appropriate. So, a new identification method based on Kullback's information criterion is proposed to deal with the non-Gaussian property. Next, the method predicting the response output probability distribution for arbitrary random input without contamination of the background noise is proposed. Here, according to original non-negative property of intensity quantity, a statistical type Laguerre series expansion is first employed as the output probability distribution form. Its expansion coefficients can be predicted by employing the above identified model. Finally, the proposed method is experimentally confirmed too by applying it to the actual sound insulation systems.
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Takahiro Ohnishi, Kogakuin University (Japan)
Michiko Kazama, Acoustic Consultant (Japan)
Mikio Tohyama, Kogakuin University (Japan)
This article describes signal estimation and detection using Multi-Windowed Short-Time Fourier Transforms (MWSTFT) and harmonics sieving. The MWSTFT proposed here analyzes a signal by using multi-rectangular windows, each of which has a different window length. The MWSTFT achieves high frequency-resolution for a short-time windowed compound signal, and the harmonics sieving estimates fundamental frequencies and their harmonics. The harmonics sieving function based on MWSTFT is powerful particularly for fundamental frequency tracking of a non-stationary signal under noisy condition. Comparison between MWSTFT and conventional STFT methods are mentioned.
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Jean S. van Eeghem, Kogakuin University (Japan)
T. Koike, NTT Advanced Technology (Japan)
Mikio Tohyama, Kogakuin University (Japan)
When the cepstrum domain contributions of a desired dry-speech signal and an unknown transfer function (TF) are divided between a low-time and a high-time region, blind dereverberation is shown to be achievable (A.V. Oppenheim, R.W. Schafer. Digital signal processing, 1975). However for a general room transfer function, the contribution to the complex cepstrum will be spread over the entire cepstrum region. The authors present a blind dereverberation method that is applicable for general types of TF's. This method is based on the fact that the contribution of the TF is fixed, i.e. compared to that of the speech, for neighboring frames. Processing the reverberant signal for short-time frames allows a recursive scheme to remove the equal TF cepstrum contributions from consecutive frames. The presented method is found to be robust for changes in the TF. Although short-time frames are processed, the effects of amply longer TF's can successfully be separated form the reverberant speech. However additional processing is required, due to noise occurrence related to short-time frame processing. When extended to semi-online processing the identification of the TF is also possible.
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Yoh-ichi Fujisaka, Kogakuin University (Japan)
Mikio Tohyama, Kogakuin University (Japan)
Akira Sugimura, Konan University (Japan)
In a 2-dimensional wave field under irreguiar shaped boundary conditions, the orbit of a sound ray has an instable chaotic motion. For wave theory, the spacing distribution of the neighboring eigenvalues is not degenerated due to the repulsion effects but follows a Wigner distribution in irregular systems. We analyze chaotic characteristics of irregular systems by both wave theory and ray theory. In wave theory, we investigate the higher eigenmodes in an irregular system by using the Finite Element Method (FEM). In ray theory, we visualize chaotic properties of the ray propagation trajectories in a chaotic wave field. As a result, it has been clarifiedthat the trajectory of the billiard problem with a stadium boundary condition has the same sensitivities to the initial conditions as does the mapping process on a logistic map does. We also discuss the transfer function between a sound source and a receiving point in the chaotic field.
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Peter O'Shea, Royal Melbourne Institute of Technology (Australia)
Simon Watkins, Royal Melbourne Institute of Technology (Australia)
Christian Peric, Royal Melbourne Institute of Technology (Australia)
Bruce Sloss, Royal Melbourne Institute of Technology (Australia)
The airflow around a moving car results in wind noise which is partially transmitted into the cabin. With the trend towards quieter cars, this wind-generated noise can dominate other noise sources. Standard methods of developing car geometries (often with the aim of minimising wind noise) are based on tests in smooth-flow wind tunnels, rather than by road trials. However, it has been noted that wind noise sounds different in the two test environments. This paper sets out to characterise these acoustical differences. Higher-order spectral statistics and wavelet analysis have been utilised and significant variations were found. Ultimately, it is hoped that such analyses can be used to compare wind noise predicted from smooth flow wind-tunnel data (utilising a knowledge of the turbulent velocity fluctuations in the atmosphere) with data measured under turbulent on-road conditions.
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Thomas Lago, University of Karlskrona/Ronneby (Sweden)
Ingvar Claesson, University of Karlskrona/Ronneby (Sweden)
An FFT analyzer is often used for spectral estimation. In theory, either a pure sinusoid or white random noise is used. In these two cases it is easy to make an estimate that is correct by using power spectra or power spectral density scaling respectively. In real life, however, signals are likely to be composed of more than one class of signals. This is especially common in the sound and vibration area. Without an a-priori information about the signal, large errors, often several hundred percent are likely. This paper addresses these estimation problems, and covers some of the theoretical background. Easy to use "rules of thumb" are given, that make it possible to verify when a correct estimation has been found. Examples are given using both authentic and synthetic. This type of problem is normally not handled in the text books, and therefore there is a need for raising this issue, especially from a practical point of view, since many engineers are not aware of the problem. From a strict theoretical point of view the problem does not exist, but in reality, if the problem is not dealt with, the consequences can be devastating.
sv970297.pdf (Scanned) TOPFengfeng Xi, Integrated Manufacturing Technologies Institute (Canada)
Presented in this paper is a graphic method called discrete holographic method which can effectively reveal distinct features from the plethora of vibration data. The method is developed based on the theory of qualitative dynamics, subject of which is to extract in a qualitative sense the characteristics of the underlying dynamics that governs the behavior of a dynamical system. The proposed discrete holographics is constructed in the three-dimensional space by three sets of vibration data called visible vectors, sampled by time delays. It is shown that the number of visible vectors sufficient for vibration signal analysis is three, which is proposed to construct the discrete holographics. The proposed method is used to analyze various types of vibration signals including transient signals, modulated signals, repetitive signals, etc. The results show that this method can effectively extract the characteristics of different types of vibration signals.
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Kam W. Lo, Defence Science and Technology Organisation (Australia)
Brian G. Ferguson, Defence Science and Technology Organisation (Australia)
For a fast moving acoustic source in proximity to a pair of widely spaced sensors, the conventional cross correlation method results in poor time delay estimates because the signal received by each sensor experiences a different degree of time scaling. The correct procedure for time delay estimation in this case is to match the time scales of the two received signals, prior to cross correlating them. In practice, the relative time scale between the two signals is not known a priori and hence it must be estimated jointly with the time delay. This can be done by evaluating the passive wideband cross-ambiguity function. Four different methods are described for computing this function. The most efficient method is applied to synthetic acoustic data which simulate the outputs of three widely spaced microphones during the low altitude transit of a jet aircraft. The resulting time delay estimates are used to calculate the angular trajectory of the aircraft during the transit.
sv970131.pdf (Scanned) TOPAlois Heiss, Bavarian Ministry of Environmental Protection (Germany)
For a quality controlled application of the percentile sound evaluation index LX , its accuracy, limited by the stochastic level fluctuations, should be quantified. This is achievable by determining first the variance of the partition of the signal ampli-tude with respect to a fixed level, the expectation value of Lx . Then the percen-tiles spread itself is accessible through the cumulative level distribution. As is still to be done, this paper presents a comprehensible proof of the partition variance formula, which is of fundamental importance for the evaluation of the Lx - confidence limits. Given a number of crossings within a given measurement time interval the probability that a definite total of the single continuous over-shoots, i. e. crossing up time intervals occurs, depends as on the stochastic systems crossings up as on its crossings down, and further on the probability density function (p. d. f.) of the crossing number. Above an easily practicable mi-nimum crossing number the p. d. f. of the total crossing time, and so of the parti-tion itself, can be presented explicitly and straightforward in microstatistic terms applying the Central Limit Theorem of Statistics. Then step by step integration of the variance definition equation leads to the already known and applied final result.
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