Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613533
Huan Wu, Zheng Bao, Kehu Yang
A unifying asymptotic performance analysis of a class of MUSIC algorithms for direction-of-arrival (DOA) estimation in fourth-order cumulant domain (FOCD-MUSIC) is presented in this paper. A simple and explicit formula for the asymptotic variances of DOA estimation by FOCD-MUSIC's is given. The Cramer-Rao bound for DOA estimation in fourth-order cumulant domain (FOCD-CRB) is also derived. The performances of three typical FOCD-MUSICs and the conventional covariance-based MUSIC are compared. It is shown that the FOCD-MUSICs are inefficient and they are not superior to the conventional MUSIC algorithm in any case. Nevertheless, the FOCD-MUSICs outperform the conventional MUSIC with reduced variances and improved robustness when the spatial sources are closely spaced and the signal-to-noise ratios (SNRs) are relatively low. Simulations are included to validate the analytical results.
{"title":"MUSICs and Cramer-Rao bound in fourth-order cumulant domain","authors":"Huan Wu, Zheng Bao, Kehu Yang","doi":"10.1109/HOST.1997.613533","DOIUrl":"https://doi.org/10.1109/HOST.1997.613533","url":null,"abstract":"A unifying asymptotic performance analysis of a class of MUSIC algorithms for direction-of-arrival (DOA) estimation in fourth-order cumulant domain (FOCD-MUSIC) is presented in this paper. A simple and explicit formula for the asymptotic variances of DOA estimation by FOCD-MUSIC's is given. The Cramer-Rao bound for DOA estimation in fourth-order cumulant domain (FOCD-CRB) is also derived. The performances of three typical FOCD-MUSICs and the conventional covariance-based MUSIC are compared. It is shown that the FOCD-MUSICs are inefficient and they are not superior to the conventional MUSIC algorithm in any case. Nevertheless, the FOCD-MUSICs outperform the conventional MUSIC with reduced variances and improved robustness when the spatial sources are closely spaced and the signal-to-noise ratios (SNRs) are relatively low. Simulations are included to validate the analytical results.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128180922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613489
N. Arthur, J. Penman
This paper proposes the use of the unnormalised bispectrum as a signal processing tool for the diagnosis of inverter-fed induction machine fault conditions. Increasingly, induction machines are supplied from nonsinusoidal, variable speed sources which increases the complexity and magnitude of the machine cage vibration. In addition, contamination of the vibration signal from both known and unknown sources makes accurate fault detection more difficult. This paper addresses both issues, experimental results are presented and it is shown that the unnormalised bispectrum improves on the diagnostic capability of more conventional second order statistical measures.
{"title":"Inverter fed induction machine condition monitoring using the bispectrum","authors":"N. Arthur, J. Penman","doi":"10.1109/HOST.1997.613489","DOIUrl":"https://doi.org/10.1109/HOST.1997.613489","url":null,"abstract":"This paper proposes the use of the unnormalised bispectrum as a signal processing tool for the diagnosis of inverter-fed induction machine fault conditions. Increasingly, induction machines are supplied from nonsinusoidal, variable speed sources which increases the complexity and magnitude of the machine cage vibration. In addition, contamination of the vibration signal from both known and unknown sources makes accurate fault detection more difficult. This paper addresses both issues, experimental results are presented and it is shown that the unnormalised bispectrum improves on the diagnostic capability of more conventional second order statistical measures.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130875895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613484
G. Gelle, M. Colas, G. Delaunay
Higher order statistics (HOS) are well suited to solving detection and classification problems because they can suppress gaussian noise and preserve some of the non-gaussian information. This paper describes the use of these methods for acoustic quality control of manufactured goods on a production line, and specifically the detection of faulty fanbelts on the drying block of a washing machine. Two HOS based methods were used in this paper. The first is based on the properties of the bispectrum in the outer triangle and particularly of the normalized bispectrum also called the skewness function. The second uses the third order cumulant of a matched filter output. This combination has the advantages of matched filtering plus the properties of higher than second order statistics making this algorithm more robust than the conventional matched filter. The method was used to classify real signals from fanbelts suffering from specific known defects.
{"title":"Higher order statistics for detection and classification of faulty fanbelts using acoustical analysis","authors":"G. Gelle, M. Colas, G. Delaunay","doi":"10.1109/HOST.1997.613484","DOIUrl":"https://doi.org/10.1109/HOST.1997.613484","url":null,"abstract":"Higher order statistics (HOS) are well suited to solving detection and classification problems because they can suppress gaussian noise and preserve some of the non-gaussian information. This paper describes the use of these methods for acoustic quality control of manufactured goods on a production line, and specifically the detection of faulty fanbelts on the drying block of a washing machine. Two HOS based methods were used in this paper. The first is based on the properties of the bispectrum in the outer triangle and particularly of the normalized bispectrum also called the skewness function. The second uses the third order cumulant of a matched filter output. This combination has the advantages of matched filtering plus the properties of higher than second order statistics making this algorithm more robust than the conventional matched filter. The method was used to classify real signals from fanbelts suffering from specific known defects.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115620222","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613478
L. Persson, J. T. Boutet
The analysis of seismicity need to be restricted to earthquakes. The estimated seismic energy release and the spatial distribution of seismic events will be erroneous and biased if the data catalogue includes artificial events such as explosions. Therefore, it is necessary to separate earthquakes and explosions prior to the compilation of the seismicity in a particular region. In the canal area of Panama, the events are equally distributed with signal energy contents in the same range, making localization and magnitude estimation not effective as discriminators. In this study we use a method based on master-event correlation's for filtering out the explosions in the seismological catalogue. We use a library of time series with the a priori knowledge of the source type. The method is based on comparison of unknown events with the library by second, third and fourth order cross-correlations. Studied time series are divided into three parts, the first phases of the P and S-wave and a window from the preceding noise. Twenty known and twenty-one unknown events are tested with master-event correlation in second, third and fourth-order domain. The second-order based method discriminate correctly 40% of the known events while the third and fourth-order based correlations succeed in 75% respectively 80% of the known cases.
{"title":"Discrimination of local seismic events in Panama by means of higher order statistics","authors":"L. Persson, J. T. Boutet","doi":"10.1109/HOST.1997.613478","DOIUrl":"https://doi.org/10.1109/HOST.1997.613478","url":null,"abstract":"The analysis of seismicity need to be restricted to earthquakes. The estimated seismic energy release and the spatial distribution of seismic events will be erroneous and biased if the data catalogue includes artificial events such as explosions. Therefore, it is necessary to separate earthquakes and explosions prior to the compilation of the seismicity in a particular region. In the canal area of Panama, the events are equally distributed with signal energy contents in the same range, making localization and magnitude estimation not effective as discriminators. In this study we use a method based on master-event correlation's for filtering out the explosions in the seismological catalogue. We use a library of time series with the a priori knowledge of the source type. The method is based on comparison of unknown events with the library by second, third and fourth order cross-correlations. Studied time series are divided into three parts, the first phases of the P and S-wave and a window from the preceding noise. Twenty known and twenty-one unknown events are tested with master-event correlation in second, third and fourth-order domain. The second-order based method discriminate correctly 40% of the known events while the third and fourth-order based correlations succeed in 75% respectively 80% of the known cases.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114929642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613528
J. How, H. Leung
The alpha-stable distribution is a theoretical model for impulsive noise that currently enjoys wide success. In this paper, we test its applicability to high resolution radars that are capable of resolving fine structure of the sea surface. The received sea clutter signal by such systems is not well modeled by a Gaussian process, and we expected that stable distributions may provide better description of noise statistics than the conventional non-Gaussian models such as the K-distribution. However, in the important for radar low probability of false alarm region, we found that the K-distribution fits better the sea-clutter amplitude statistics than the alpha-stable distribution. In the application considered, we explain this failure of the stable model based on the analytical stable noise modeling.
{"title":"No evidence of stable distributions in radar clutter","authors":"J. How, H. Leung","doi":"10.1109/HOST.1997.613528","DOIUrl":"https://doi.org/10.1109/HOST.1997.613528","url":null,"abstract":"The alpha-stable distribution is a theoretical model for impulsive noise that currently enjoys wide success. In this paper, we test its applicability to high resolution radars that are capable of resolving fine structure of the sea surface. The received sea clutter signal by such systems is not well modeled by a Gaussian process, and we expected that stable distributions may provide better description of noise statistics than the conventional non-Gaussian models such as the K-distribution. However, in the important for radar low probability of false alarm region, we found that the K-distribution fits better the sea-clutter amplitude statistics than the alpha-stable distribution. In the application considered, we explain this failure of the stable model based on the analytical stable noise modeling.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117084613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613553
S. Bates, S. McLaughlin
This paper concerns the estimation of the parameters that describe a stable distribution. Stable distributions are characterised by four parameters which can be estimated using a number of methods and although approximate maximum likelihood estimation (MLE) techniques do exist, they are computationally intensive. There are a number of techniques that are much faster than MLE and these are the focus of this paper. These techniques are compared and contrasted both for stable random variables and for teletraffic data.
{"title":"The estimation of stable distribution parameters","authors":"S. Bates, S. McLaughlin","doi":"10.1109/HOST.1997.613553","DOIUrl":"https://doi.org/10.1109/HOST.1997.613553","url":null,"abstract":"This paper concerns the estimation of the parameters that describe a stable distribution. Stable distributions are characterised by four parameters which can be estimated using a number of methods and although approximate maximum likelihood estimation (MLE) techniques do exist, they are computationally intensive. There are a number of techniques that are much faster than MLE and these are the focus of this paper. These techniques are compared and contrasted both for stable random variables and for teletraffic data.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126212150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613541
D. Korze, D. Zazula
The paper deals with the variance analysis estimating the third-order cumulant of the MA system output signal which was excited with Bernoulli distributed white noise on the input. These scheme was used to simulate the superimposed systems, or signals, which often arise in the practical approaches (EMG signal decomposition). The equations were derived which show dependencies of the variances of the third-order output cumulant values on the length of the output signal and on the values of the samples in the impulse response of the unknown system as well. The structure of the variance inside the third-order cumulant array was observed. The speed and the convergence of the identification procedure could be predicted using these results for the case of superimposed MA systems. The knowledge of the structure of the variance is helpful in designing new identification methods. Some examples are given to show the correctness of the derived equations.
{"title":"Identifiability of the superimposed signals using third-order cumulants","authors":"D. Korze, D. Zazula","doi":"10.1109/HOST.1997.613541","DOIUrl":"https://doi.org/10.1109/HOST.1997.613541","url":null,"abstract":"The paper deals with the variance analysis estimating the third-order cumulant of the MA system output signal which was excited with Bernoulli distributed white noise on the input. These scheme was used to simulate the superimposed systems, or signals, which often arise in the practical approaches (EMG signal decomposition). The equations were derived which show dependencies of the variances of the third-order output cumulant values on the length of the output signal and on the values of the samples in the impulse response of the unknown system as well. The structure of the variance inside the third-order cumulant array was observed. The speed and the convergence of the identification procedure could be predicted using these results for the case of superimposed MA systems. The knowledge of the structure of the variance is helpful in designing new identification methods. Some examples are given to show the correctness of the derived equations.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120937516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613561
D. Leporini, J. Pesquet
In many applications it is necessary to characterize the statistical properties of the wavelet/wavelet packet coefficients of a stationary random signal. This problem is typically encountered in denoising methods using wavelet packets. Then, in a stationary non-Gaussian noise scenario, it may be useful to determine the high-order statistics of the wavelet packet coefficients. In this work, we prove that this task may be performed through multidimensional filter banks. In particular we show how the cumulants of the M-band wavelet packet coefficients of a strictly stationary signal are derived from those of the signal and we provide recursive decomposition and reconstruction formulae to compute the cumulants of these coefficients. High-order wavelet packets, associated to multidimensional filter banks, are presented along with some of their properties. Finally, the asymptotic normality of the coefficients is proved.
{"title":"High-order properties of M-band wavelet packet decompositions","authors":"D. Leporini, J. Pesquet","doi":"10.1109/HOST.1997.613561","DOIUrl":"https://doi.org/10.1109/HOST.1997.613561","url":null,"abstract":"In many applications it is necessary to characterize the statistical properties of the wavelet/wavelet packet coefficients of a stationary random signal. This problem is typically encountered in denoising methods using wavelet packets. Then, in a stationary non-Gaussian noise scenario, it may be useful to determine the high-order statistics of the wavelet packet coefficients. In this work, we prove that this task may be performed through multidimensional filter banks. In particular we show how the cumulants of the M-band wavelet packet coefficients of a strictly stationary signal are derived from those of the signal and we provide recursive decomposition and reconstruction formulae to compute the cumulants of these coefficients. High-order wavelet packets, associated to multidimensional filter banks, are presented along with some of their properties. Finally, the asymptotic normality of the coefficients is proved.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116111553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613552
J. Le Roux, C. Huet
This communication presents a necessary and sufficient condition for the factorizability of higher order spectra of complex signals. This condition is based on the symmetries of higher order spectra and on an extension of a formula proposed by Marron, Sanchez and Sullivan for unwrapping phases of third order spectra (see J. Opt. Soc. Am. A, vol.7, p.14-20, 1990). It is an identity between products of higher order spectra. Our factorisability test requires no phase unwrapping.
{"title":"Factorizability of complex signals higher (even) order spectra: a necessary and sufficient condition","authors":"J. Le Roux, C. Huet","doi":"10.1109/HOST.1997.613552","DOIUrl":"https://doi.org/10.1109/HOST.1997.613552","url":null,"abstract":"This communication presents a necessary and sufficient condition for the factorizability of higher order spectra of complex signals. This condition is based on the symmetries of higher order spectra and on an extension of a formula proposed by Marron, Sanchez and Sullivan for unwrapping phases of third order spectra (see J. Opt. Soc. Am. A, vol.7, p.14-20, 1990). It is an identity between products of higher order spectra. Our factorisability test requires no phase unwrapping.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"17 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121016510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613548
P. Chevalier, V. Capdevielle, P. Comon
Over the last decade, higher order (HO) methods have been strongly developed in particular to blindly separate instantaneous mixtures of statistically independent stationary sources. However, in many situations of practical interest, the received sources are (quasi)-cyclostationary (digital radiocommunications) and are not always statistically independent but may be correlated to each other, which occurs in particular for HF links or in mobile radiocommunications contexts where propagation multipaths are omnipresent. In such situations, the behaviour of the classical HO blind source separation methods is not known, which may be a limitation to the use of these methods in operational contexts. The purpose of this paper is precisely to fill the gap previously mentioned by analysing the behaviour, in radiocommunications contexts, of three classical HO blind source separation methods when several potentially correlated paths of each source, assumed (quasi)-cyclostationary, are received by the array.
{"title":"Behaviour of higher order blind source separation methods in the presence of cyclostationary correlated multipaths","authors":"P. Chevalier, V. Capdevielle, P. Comon","doi":"10.1109/HOST.1997.613548","DOIUrl":"https://doi.org/10.1109/HOST.1997.613548","url":null,"abstract":"Over the last decade, higher order (HO) methods have been strongly developed in particular to blindly separate instantaneous mixtures of statistically independent stationary sources. However, in many situations of practical interest, the received sources are (quasi)-cyclostationary (digital radiocommunications) and are not always statistically independent but may be correlated to each other, which occurs in particular for HF links or in mobile radiocommunications contexts where propagation multipaths are omnipresent. In such situations, the behaviour of the classical HO blind source separation methods is not known, which may be a limitation to the use of these methods in operational contexts. The purpose of this paper is precisely to fill the gap previously mentioned by analysing the behaviour, in radiocommunications contexts, of three classical HO blind source separation methods when several potentially correlated paths of each source, assumed (quasi)-cyclostationary, are received by the array.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121363112","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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