Pub Date : 1997-07-21DOI: 10.1109/HOST.1997.613551
K. Chandrasekhar, S. Joshi
A generalised predictor space representation (of nonlinearity order two and memory M) for nonGaussian and nonminimum phase ARMA processes is proposed here, by expanding the underlying Hilbert space of finite L/sub 2/ norm random variables, which is now composed of linear combinations of linear as well as second order nonlinear terms of the process samples. Here the higher order statistical information enters into the picture in a natural way through the nonlinear terms. It is expected that the geometrical structure provided by the proposed predictor space would simplify the modeling of these processes. A set of new innovation vectors is defined on this space. Some of the properties of the new space are presented. The finite dimensionality of the proposed predictor space, when the underlying process admits a nonGaussian and nonminimum phase ARMA representation is proved. The application of the proposed theory to estimate nonGaussian and nonminimum phase ARMA process parameters is also discussed.
{"title":"On representation for nonGaussian ARMA processes","authors":"K. Chandrasekhar, S. Joshi","doi":"10.1109/HOST.1997.613551","DOIUrl":"https://doi.org/10.1109/HOST.1997.613551","url":null,"abstract":"A generalised predictor space representation (of nonlinearity order two and memory M) for nonGaussian and nonminimum phase ARMA processes is proposed here, by expanding the underlying Hilbert space of finite L/sub 2/ norm random variables, which is now composed of linear combinations of linear as well as second order nonlinear terms of the process samples. Here the higher order statistical information enters into the picture in a natural way through the nonlinear terms. It is expected that the geometrical structure provided by the proposed predictor space would simplify the modeling of these processes. A set of new innovation vectors is defined on this space. Some of the properties of the new space are presented. The finite dimensionality of the proposed predictor space, when the underlying process admits a nonGaussian and nonminimum phase ARMA representation is proved. The application of the proposed theory to estimate nonGaussian and nonminimum phase ARMA process parameters is also discussed.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"38 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":"131556367","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.1997.613498
Ying-Chang Liang, A. R. Leyman, Xianda Zhang
This paper addresses the problem of (almost) periodic moving average (APMA) system identification. Two normal equations are established by using time varying higher order cumulants of the measurements, from which two new linear algebraic algorithms are presented for parameter estimation. Simulation examples are given to demonstrate the performance of these new approaches.
{"title":"Linear algebraic approaches for (almost) periodic moving average system identification","authors":"Ying-Chang Liang, A. R. Leyman, Xianda Zhang","doi":"10.1109/HOST.1997.613498","DOIUrl":"https://doi.org/10.1109/HOST.1997.613498","url":null,"abstract":"This paper addresses the problem of (almost) periodic moving average (APMA) system identification. Two normal equations are established by using time varying higher order cumulants of the measurements, from which two new linear algebraic algorithms are presented for parameter estimation. Simulation examples are given to demonstrate the performance of these new approaches.","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":"114419976","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.1997.613526
J.G. Gonzalez, D. W. Griffith, G. Arce
Techniques based on conventional higher-order statistics fail when the underlying processes become impulsive. Although methods based on fractional lower-order statistics (FLOS) have proven successful in dealing with heavy-tailed processes, they fail in general when the noise distribution has very heavy algebraic tails, i.e., when the algebraic tail constant is close to zero. In this paper we introduce a signal processing framework that we call zero-order statistics (ZOS). ZOS are well defined for any process with algebraic or lighter tails, including the full class of /spl alpha/-stable distributions. We introduce zero-order scale and location statistics and study several of their properties. The intimate link between ZOS and FLOS is presented. We also show that ZOS are the optimal framework when the underlying processes are very impulsive. All figures, simulations and source code utilized in this paper are reproducible and freely accessible in the Internet at http://www.ee.udel./edu//sup /spl sim//gonzalez/PUBS/HOS97a.
{"title":"Zero-order statistics: a signal processing framework for very impulsive processes","authors":"J.G. Gonzalez, D. W. Griffith, G. Arce","doi":"10.1109/HOST.1997.613526","DOIUrl":"https://doi.org/10.1109/HOST.1997.613526","url":null,"abstract":"Techniques based on conventional higher-order statistics fail when the underlying processes become impulsive. Although methods based on fractional lower-order statistics (FLOS) have proven successful in dealing with heavy-tailed processes, they fail in general when the noise distribution has very heavy algebraic tails, i.e., when the algebraic tail constant is close to zero. In this paper we introduce a signal processing framework that we call zero-order statistics (ZOS). ZOS are well defined for any process with algebraic or lighter tails, including the full class of /spl alpha/-stable distributions. We introduce zero-order scale and location statistics and study several of their properties. The intimate link between ZOS and FLOS is presented. We also show that ZOS are the optimal framework when the underlying processes are very impulsive. All figures, simulations and source code utilized in this paper are reproducible and freely accessible in the Internet at http://www.ee.udel./edu//sup /spl sim//gonzalez/PUBS/HOS97a.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"86 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":"123102337","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.1997.613529
A. Karasaridis, D. Hatzinakos
We present a new model for aggregated network traffic based on /spl alpha/-stable self-similar processes which captures the burstiness and the long range dependence of the data. We show how the fractional Gaussian noise assumption fails and why our proposed model fits well by comparing real and synthesized network traffic. In addition, we show that we can speed up the simulation times for estimation of rare event probabilities, such as cell losses in ATM switches, by up to three orders of magnitude using /spl alpha/-stable modeling and importance sampling.
{"title":"On the modeling of network traffic and fast simulation of rare events using /spl alpha/-stable self-similar processes","authors":"A. Karasaridis, D. Hatzinakos","doi":"10.1109/HOST.1997.613529","DOIUrl":"https://doi.org/10.1109/HOST.1997.613529","url":null,"abstract":"We present a new model for aggregated network traffic based on /spl alpha/-stable self-similar processes which captures the burstiness and the long range dependence of the data. We show how the fractional Gaussian noise assumption fails and why our proposed model fits well by comparing real and synthesized network traffic. In addition, we show that we can speed up the simulation times for estimation of rare event probabilities, such as cell losses in ATM switches, by up to three orders of magnitude using /spl alpha/-stable modeling and importance sampling.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"2015 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":"121658000","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.1997.613538
L. De Lathauwer, B. De Moor, J. Vandewalle
Most algebraic methods for independent component analysis (ICA) consist of a second-order and a higher-order stage. The former can be considered as a classical principal component analysis (PCA), with a three-fold goal: (a) reduction of the parameter set of unknowns to the manifold of orthogonal matrices, (b) standardization of the unknown source signals to mutually uncorrelated unit-variance signals, and (c) determination of the number of sources. In the higher-order stage the remaining unknown orthogonal factor is determined by imposing statistical independence on the source estimates. Like all correlation-based techniques, this set-up has the disadvantage that it is affected by additive Gaussian noise. However it is possible to solve the problem, in a way that is conceptually blind to additive Gaussian noise, by resorting only to higher-order cumulants. The purpose of this paper is to explain how the dimensionality of the ICA-model can algebraically be reduced to the true number of sources in higher-order-only schemes.
{"title":"Dimensionality reduction in higher-order-only ICA","authors":"L. De Lathauwer, B. De Moor, J. Vandewalle","doi":"10.1109/HOST.1997.613538","DOIUrl":"https://doi.org/10.1109/HOST.1997.613538","url":null,"abstract":"Most algebraic methods for independent component analysis (ICA) consist of a second-order and a higher-order stage. The former can be considered as a classical principal component analysis (PCA), with a three-fold goal: (a) reduction of the parameter set of unknowns to the manifold of orthogonal matrices, (b) standardization of the unknown source signals to mutually uncorrelated unit-variance signals, and (c) determination of the number of sources. In the higher-order stage the remaining unknown orthogonal factor is determined by imposing statistical independence on the source estimates. Like all correlation-based techniques, this set-up has the disadvantage that it is affected by additive Gaussian noise. However it is possible to solve the problem, in a way that is conceptually blind to additive Gaussian noise, by resorting only to higher-order cumulants. The purpose of this paper is to explain how the dimensionality of the ICA-model can algebraically be reduced to the true number of sources in higher-order-only schemes.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"24 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":"116686349","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.1997.613485
C. Martret, Pierre Marchand, J. Lacoume
The search for discriminating features is a crucial point when a modulation classification task is aimed. This paper introduces new features based on a combination of fourth- and second-order temporal cyclic cumulants. Such a combination enhances the theoretical discrimination that can be achieved by a single stationary cumulant, and moreover, the cyclic parameters become discriminating whereas it is not the case when they are considered at pure orders. As an application, we propose a process to classify 4-PSK vs. 16-QAM modulations. The classification is achieved by estimating the feature for the received signal, and comparing it with theoretical ones by a matched filter technique. Simulations show that though the cyclic parameters are a priori more discriminating than their stationary counterparts, the variance of their estimates may overcome this advantage.
{"title":"Classification of linear modulations by a combination of different orders cyclic cumulants","authors":"C. Martret, Pierre Marchand, J. Lacoume","doi":"10.1109/HOST.1997.613485","DOIUrl":"https://doi.org/10.1109/HOST.1997.613485","url":null,"abstract":"The search for discriminating features is a crucial point when a modulation classification task is aimed. This paper introduces new features based on a combination of fourth- and second-order temporal cyclic cumulants. Such a combination enhances the theoretical discrimination that can be achieved by a single stationary cumulant, and moreover, the cyclic parameters become discriminating whereas it is not the case when they are considered at pure orders. As an application, we propose a process to classify 4-PSK vs. 16-QAM modulations. The classification is achieved by estimating the feature for the received signal, and comparing it with theoretical ones by a matched filter technique. Simulations show that though the cyclic parameters are a priori more discriminating than their stationary counterparts, the variance of their estimates may overcome this advantage.","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":"128613895","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.1997.613544
C. Servière, V. Capdevielle, J. Lacoume
A particular source separation problem is addressed in this paper. We mainly focus on the separation of convolutive mixtures of rotating machine noises when the rotation speeds are close. Three specific points are developed. In the first point, we study the feasibility of the separation of periodic signals, regarding the hypothesis of random and non gaussian sources. We also discuss about the hypothesis of independence between the sources, as a function of the rotation speeds. In the second point, we analyze the performances of the source separation for close rotation speeds. They are linked to a partial correlation between the machine noises. Then, we propose a new method for very close rotation speeds, which takes into account this partial dependence between the sources.
{"title":"Separation of sinusoidal sources","authors":"C. Servière, V. Capdevielle, J. Lacoume","doi":"10.1109/HOST.1997.613544","DOIUrl":"https://doi.org/10.1109/HOST.1997.613544","url":null,"abstract":"A particular source separation problem is addressed in this paper. We mainly focus on the separation of convolutive mixtures of rotating machine noises when the rotation speeds are close. Three specific points are developed. In the first point, we study the feasibility of the separation of periodic signals, regarding the hypothesis of random and non gaussian sources. We also discuss about the hypothesis of independence between the sources, as a function of the rotation speeds. In the second point, we analyze the performances of the source separation for close rotation speeds. They are linked to a partial correlation between the machine noises. Then, we propose a new method for very close rotation speeds, which takes into account this partial dependence between the sources.","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":"128946866","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.1997.613502
T. Stathaki
This paper forms a part of a series of studies we have undertaken, where the problem of nonlinear signal modelling is examined. We assume that the observed "output" signal is derived from a Volterra filter that is driven by a Gaussian input. Both the filter parameters and the input signal are unknown and therefore the problem can be classified as blind or unsupervised in nature. In the statistical approach to the solution of the above problem we seek for equations that relate the unknown parameters of the Volterra model with the statistical parameters of the "output" signal to be modelled. These equations are highly nonlinear and their solution is achieved through a novel constrained optimisation formulation. The results of the entire modelling scheme are compared with other contributions.
{"title":"Nonlinearly constrained optimisation using a penalty-transformation method for Volterra parameter estimation","authors":"T. Stathaki","doi":"10.1109/HOST.1997.613502","DOIUrl":"https://doi.org/10.1109/HOST.1997.613502","url":null,"abstract":"This paper forms a part of a series of studies we have undertaken, where the problem of nonlinear signal modelling is examined. We assume that the observed \"output\" signal is derived from a Volterra filter that is driven by a Gaussian input. Both the filter parameters and the input signal are unknown and therefore the problem can be classified as blind or unsupervised in nature. In the statistical approach to the solution of the above problem we seek for equations that relate the unknown parameters of the Volterra model with the statistical parameters of the \"output\" signal to be modelled. These equations are highly nonlinear and their solution is achieved through a novel constrained optimisation formulation. The results of the entire modelling scheme are compared with other contributions.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"9 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":"116867534","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.1997.613521
Jijun Yin, A. Petropulu
A method is presented for blind system identification in an impulsive environment, where the system output is described by a symmetric /spl alpha/-stable (S/spl alpha/S) law. The method employs either the phase or the magnitude of the recently proposed /spl alpha/-spectrum of the system output. It is much simpler than the method proposed previously which also relies on the phase or magnitude of the /spl alpha/-spectrum, and provides the system cepstrum via closed form expressions.
{"title":"Blind system identification in an impulsive environment","authors":"Jijun Yin, A. Petropulu","doi":"10.1109/HOST.1997.613521","DOIUrl":"https://doi.org/10.1109/HOST.1997.613521","url":null,"abstract":"A method is presented for blind system identification in an impulsive environment, where the system output is described by a symmetric /spl alpha/-stable (S/spl alpha/S) law. The method employs either the phase or the magnitude of the recently proposed /spl alpha/-spectrum of the system output. It is much simpler than the method proposed previously which also relies on the phase or magnitude of the /spl alpha/-spectrum, and provides the system cepstrum via closed form expressions.","PeriodicalId":305928,"journal":{"name":"Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics","volume":"3 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":"115213270","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.1997.613537
M. Hirari, M. Hayakawa
We propose a new approach for the estimation of DOA for polarized EM waves using blind separation of sources. In this approach we use a vector-sensor, a sensor whose output is a complete set of the EM field components of the irradiating wave and we reconstruct the waveforms of all the original signals; that is, all the EM components of the source's field. The blind separation of sources is made iteratively using a recurrent Hopfield-like single layer neural network. The simulation results for two sources have been investigated. We have considered coherent and incoherent sources, and also the case of varying DOA's vis-a-vis to the sensor and a varying polarization.
{"title":"DOA estimation using blind separation of sources","authors":"M. Hirari, M. Hayakawa","doi":"10.1109/HOST.1997.613537","DOIUrl":"https://doi.org/10.1109/HOST.1997.613537","url":null,"abstract":"We propose a new approach for the estimation of DOA for polarized EM waves using blind separation of sources. In this approach we use a vector-sensor, a sensor whose output is a complete set of the EM field components of the irradiating wave and we reconstruct the waveforms of all the original signals; that is, all the EM components of the source's field. The blind separation of sources is made iteratively using a recurrent Hopfield-like single layer neural network. The simulation results for two sources have been investigated. We have considered coherent and incoherent sources, and also the case of varying DOA's vis-a-vis to the sensor and a varying polarization.","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":"115317201","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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