{"title":"Discrete rotational Gabor transform","authors":"A. Akan, L. Chaparro","doi":"10.1109/TFSA.1996.547208","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547208","url":null,"abstract":"In this paper, we present a discrete rotational Gabor transform and apply it to signal representation on a non-rectangular time-frequency plane tiling. We use a modified version of the recently proposed discrete rotational Fourier transform. The rotational Gabor transform decomposes a signal using as basis functions scaled, translated and modulated by linear chirps windows. As a result, the time-varying frequency content of a signal is represented better than with sinusoidal modulated expansions. For a multi-component signal, the Gabor coefficients are obtained by combining different tilings to maximize a local energy concentration measure. This permits us to achieve a highly localized time-frequency signal representation. Examples are given to illustrate the transformation.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127447511","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}
{"title":"Diagonalization of the auto-correlation functions of random signals in terms of Cauchy wavelets using operator algebra","authors":"F. Sakaguchi","doi":"10.1109/TFSA.1996.546692","DOIUrl":"https://doi.org/10.1109/TFSA.1996.546692","url":null,"abstract":"The eigenfunction system of a kind of operator is identical to the over-complete Cauchy wavelet system, as has been shown previously. In this presentation, the re-ordering problem among this operator and its adjoint is investigated. Then, an application of this re-ordering problem to the pseudo-diagonalization problem of the autocorrelation function of a stochastic process is proposed.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126944284","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}
{"title":"Rational transfer matrices with FIR inverses","authors":"C. Brislawn","doi":"10.1109/TFSA.1996.546684","DOIUrl":"https://doi.org/10.1109/TFSA.1996.546684","url":null,"abstract":"We present a simple extension for rational transfer matrices of known results characterizing the invariant factors of causal FIR matrices with FIR inverses. This includes and generalizes previous characterizations of causal FIR multirate filter banks with anticausal FIR inverses, the so-called cafacafi systems. In particular, we extend (to the rational case) the result that G(z) is a square cafacafi system if and only if its determinantal degree is equal to its McMillan degree.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127788862","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}
{"title":"Examination of wavelet packet signal sets for over-saturated multiple access communications","authors":"R. Learned, H. Krim, A. Willsky","doi":"10.1109/TFSA.1996.550077","DOIUrl":"https://doi.org/10.1109/TFSA.1996.550077","url":null,"abstract":"This paper addresses the problem of signature set design for uncoded multiple access (MA) communication in which user signature waveforms are linearly dependent. In general, the linearly dependent or \"over-saturated\" scenario requires an exponentially complex detector. The introduction of an optimal tree-structured joint detector of extremely low complexity has sparked our interest in signature set choice for over-saturated MA communications. The tree detector requires the set of linearly dependent user signatures to have tree-structured cross-correlations. This design guideline is a natural by-product of redundant wavelet packet signals. In this paper we explore, via simulations, the performance of wavelet packet signature sets and find them to do very well in general and to offer promising behavior with the introduction of arbitrary carrier phase.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124306332","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}
{"title":"Evolutive instantaneous spectrum associated with the partial autocorrelation function for nonstationary time series","authors":"S. Dégerine, S. Lambert","doi":"10.1109/TFSA.1996.550091","DOIUrl":"https://doi.org/10.1109/TFSA.1996.550091","url":null,"abstract":"The partial autocorrelation function (PACF) of a nonstationary time series is presented. This function characterizes the second order properties of the process but is easily identifiable by comparison with the classical autocovariance function (ACF) which must be nonnegative definite (n.n.d.). As in the stationary case, this parametrization is well adapted to the autoregressive processes. It is also an elegant tool for studying the periodically correlated processes. Nevertheless, our main result is the introduction of a new time-dependent power spectrum clearly related to the PACF. At each time, this spectrum describes a stationary situation in which the present is correlated with the past in the same way as our nonstationary process at this time. The properties of this spectrum are analyzed and the comparison with two similar other spectra is made. Sampled Brownian motion and linear \"chirps\" are considered for illustration.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129691714","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}
{"title":"Signal waveform restoration by wavelet denoising","authors":"S.Q. Wu, P. C. Ching","doi":"10.1109/TFSA.1996.546693","DOIUrl":"https://doi.org/10.1109/TFSA.1996.546693","url":null,"abstract":"In this paper, we first establish an approximated sampling theorem for an arbitrary continuous signal which is essential for wavelet analysis. The differences and similarities between quadrature mirror filter decomposition and wavelet decomposition are contrasted. We then propose an efficient way to recover a source signal buried in white noise by using wavelet denoising. The method is capable of reducing the mean square error bound from O(log/sup 2/(n)) to O(log(n)), where n is the number of samples. It is also shown that the new estimator is asymptotically unbiased if the source signal is a piece-wise polynomial.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133197396","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}
{"title":"Time-correlation analysis of nonstationary signals with application to speech processing","authors":"Ta‐Hsin Li, J. Gibson","doi":"10.1109/TFSA.1996.550089","DOIUrl":"https://doi.org/10.1109/TFSA.1996.550089","url":null,"abstract":"This paper proposes a new method of displaying and analyzing the evolutionary correlation structure of nonstationary signals. The method, called time-correlation analysis (TCA), is based on a filter-bank approach for stochastic signal characterization known as parametric filtering. Some properties of the TCA method are discussed that can be used to interpret the TCA plot. Examples of an application to speech analysis are given.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131202031","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}
{"title":"Applications of Wigner-Ville distribution on ERS-1 SAR images","authors":"S. Grassin, R. Garello","doi":"10.1109/TFSA.1996.547471","DOIUrl":"https://doi.org/10.1109/TFSA.1996.547471","url":null,"abstract":"We propose here some utilizations of the Wigner-Ville distribution (WVD) for analysing ocean SAR images. It can be used for different purposes, the first one being the specific ability of the WVD for spectral analysis, especially with non-stationary signals. A second possible use is in the detection of roughness variations of the ocean surface, via the decrease of the spectrum around its maximum. It allows for instance automatic detection of oil slick or floes.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"206 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132093665","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}
{"title":"Improve the quality of diagnostic parameters of an electronystagmogram using signal filtration in the time-frequency domain and adaptatively adjusted characteristics","authors":"P. Augustyniak, R. Tadeusiewicz","doi":"10.1109/TFSA.1996.550072","DOIUrl":"https://doi.org/10.1109/TFSA.1996.550072","url":null,"abstract":"The present study introduces the application of adaptative signal filtration in the time-frequency domain for the determination of the ENG (electronystagmogram) diagnostic parameters. In commonly used methods, the imprecision in phases delimitation-caused by constant-characteristics signal filtration-is the main source of inaccuracies in diagnostic parameters. Since the signal is very fragile and the acquisition conditions are not stable in time, the need for adaptive filtration seems to be evident. The use of the reversible wavelet transform of the ENG signal makes it possible to modify each \"atom\" of signal independently. A significant improvement in quality of the calculated diagnostic parameters has been achieved, expressed by a simultaneous occurrence of minimum inaccuracies and a minimum number of interpretation errors.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133592133","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}
{"title":"The effect of mismatching analysis signals and time-frequency representations","authors":"A. Papandreou-Suppappola, G. Boudreaux-Bartels","doi":"10.1109/TFSA.1996.546708","DOIUrl":"https://doi.org/10.1109/TFSA.1996.546708","url":null,"abstract":"We study the time-frequency geometry underlying quadratic time-frequency representations (QTFRs) defined based on a generalized time-shift covariance property. These QTFRs include the generalized warped Wigner distribution (WD) and its smoothed versions that are useful for reducing cross terms in multicomponent signal analysis applications. The generalized warped WD is ideal for analyzing nonstationary signals whose group delay matches the specified time-shift covariance. Its smoothed versions may also be well suited for various signals provided that their smoothing characteristics match the signal's time-frequency structure. Thus, we examine the effects of a mismatch between the analysis signal and the chosen QTFR. We provide examples to demonstrate the advantage of matching the signal's group delay with the generalized time-shift covariance property of a given class of QTFRs, and to demonstrate that mismatch can cause significant distortion.","PeriodicalId":415923,"journal":{"name":"Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130241594","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}