Showing papers on "Time–frequency analysis published in 1989"
01 Jan 1989
TL;DR: Nonstationary signals have a time-dependent spectral content and require joint time—frequency representations, which are in contrast to stationary signals whose energy spectrum characterizes their spectralcontent and that is independent of time.
Abstract: Nonstationary signals have a time-dependent spectral content. This is in contrast to stationary signals whose energy spectrum characterizes their spectral content and that is independent of time. Therefore, nonstationary signals require joint time—frequency representations.
66 citations
01 Jan 1989
TL;DR: Most of the Signal Processing methods which have been proposed in this direction are reviewed, with emphasis on time-frequency representations and on their time-scale versions which implicitly make use of “wavelet” concepts.
Abstract: The analysis and the processing of nonstationary signals call for specific tools which go beyond Fourier analysis. This paper is intended to review most of the Signal Processing methods which have been proposed in this direction. Emphasis is put on time-frequency representations and on their time-scale versions which implicitly make use of “wavelet” concepts. Relationships between Gabor expansion, wavelet transform and ambiguity functions are detailed by considering signal decomposition as a detection-estimation problem. This permits one to make more precise some of the links which exist between time-frequency and time-scale.
46 citations
08 May 1989
TL;DR: In this paper, a procedure for the time-frequency analysis of signals, based on timefrequency distributions (TFDs) and instantaneous frequency (IF) estimation, is described, and the relationship of these estimators to others based on the central finite difference of the phase of the analytic signal is given.
Abstract: A procedure is described for the time-frequency analysis of signals, based on time-frequency distributions (TFDs) and instantaneous frequency (IF) estimation. First, a suitable TFD is used to determine the number of signal components. Then, if the signal is monocomponent, the IF law can be estimated directly. For multicomponent signals, two-dimensional windowing in the time-frequency domain (a form of time-varying filtering) is used to isolate each component; IF estimation is then applied to the individual components. The periodic first moment of a TFD is used to estimate the IF. A suitable definition and of the periodic first moment is proposed, and the relationship of these estimators to others based on the central finite difference of the phase of the analytic signal is given. A TFD such as the Wigner-Ville distribution can be used to represent both IF and amplitude variations in the individual signal components at each stage of the analysis. >
31 citations
08 May 1989
TL;DR: In this article, a discussion of instantaneous frequency from the point of view of joint time-frequency distributions is presented, which forces the consideration of the standard deviation of the instantaneous frequency at a given time.
Abstract: A discussion of instantaneous frequency from the point of view of joint time-frequency distributions is presented. From this perspective, instantaneous frequency is the average frequency at a particular time. This view forces the consideration of the standard deviation of instantaneous frequency at a given time. The authors consider these issues and argue that this approach is plausible and clarifies other issues, particularly the description of a multicomponent signal. >
18 citations
01 Jan 1989
TL;DR: In this paper, the affine group of clock changes is used as the basic group of signal theory, and the general affine covariant joint distributions are considered, and a subclass is singled out by its interesting properties: it reduces to Wigner-Ville's function when applied to narrowband signals, it gives the spectrum by time integration, and it is time-localized if applied to a timelocalized signal.
Abstract: The usual time-frequency representations corresponding to the group of time and frequency translations are shown to give rise to time-localization anomalies. Instead, the affine group of clock changes is used as the basic group of signal theory, and the general affine covariant joint distributions are considered. A subclass is singled out by its interesting properties: it reduces to Wigner-Ville's function when applied to narrowband signals, it gives the spectrum by time integration, and it is time-localized when applied to a time-localized signal. >
6 citations
14 Nov 1989
TL;DR: It is shown that Zak transform is a major tool in analysis and synthesis of non-stationary signals.
Abstract: A Zak transform is defined which plays a role in wavelet analysis based on the affine group completely analogous to the role played by the Zak transform on the wavelet analysis based on the Weyl-Heisenberg group. It is shown that Zak transform is a major tool in analysis and synthesis of non-stationary signals.
4 citations
14 Nov 1989
TL;DR: The Q-distribution as discussed by the authors is a modified Wigner-Ville representation that is related to the wideband ambiguity function by an integral transform and can be used to construct a proportional bandwidth spectrogram corresponding to a bank of constant-Q filters.
Abstract: The Wigner-Ville (W-V) distribution is a time-frequency representation that yields a highly accurate estimate of instantaneous frequency. It is related to the narrowband ambiguity function by an integral transform, and it can be used in a variety of detection and estimation problems. Convolution of signal and filter W-V distributions yields a spectrogram that could also be constructed with a bank of constant bandwidth filters. The wideband, ambiguity function represents the Doppler effect with dilation or compression rather than with frequency shift as in the narrowband approximation. The "Q-distribution" is a modified W-V representation that is related to the wideband ambiguity function by an integral transform and can be used to construct a proportional bandwidth spectrogram corresponding to a bank of constant-Q filters. The Q-distribution is thus a wideband version of the W-V distribution. Properties of the Q-distribution indicate that it may prove useful for detection and parameter estimation as well as measurement of wideband scattering functions.
3 citations
08 May 1989
TL;DR: A detailed description of the hybrid implementation of a fully programmable nonbaseband time- frequencies processor is given, capable of implementing discrete versions of Cohen class functions, including the Wigner distribution and the ambiguity function and other time-frequency analysis techniques in real time.
Abstract: A detailed description of the hybrid implementation of a fully programmable nonbaseband time-frequency processor is given. This processor is capable of implementing discrete versions of Cohen class functions, including the Wigner distribution and the ambiguity function and other time-frequency analysis techniques in real time. This implementation combines a wideband digital receiver and signal and control processors in dense circuits to allow the real-time capture and analysis of signals at sample rates of up to 40 MHz. The wideband digital receiver efficiently translates a narrowband signal of interest to baseband, filters it using Hogenauer filter techniques, and decimates it by a programmable rate. The resulting sampled data are then processed with a specified time-frequency algorithm. The dynamic range of the digital processing is in excess of 90 dB with frequency resolutions of less than 0.1 Hz. This dynamic range is beyond the current capabilities of analog-to-digital converters at the higher sampling rates. The implementation can process either real or complex signals. >
1 citations
01 Jan 1989
TL;DR: The paper presents computer procedures used for discrete TF signal processing which are based on the auto WVD (computation of an analytic signal, computation of the auto pseudo (un)smoothed WVD and signal synthesis from the modified WV-spectrum).
Abstract: In nonstationary case two-dimensional signal processing in mixed time-frequency (TF) domain can have a lot of advantages over one-dimensional processing only in time or only in frequency. It is especially true, when as a mixed time-frequency signal representation the high resolution Wigner-Ville distribution (WVD) is used. The paper presents computer procedures used for discrete TF signal processing which are based on the auto WVD (computation of an analytic signal, computation of the auto pseudo (un)smoothed WVD and signal synthesis from the modified WV-spectrum). They are assigned for general purpose computers and make use of routines from a standard mathematical library.
1 citations