Showing papers on "Time–frequency analysis published in 1988"
TL;DR: It is shown that a correct use of the Wigner distribution for time-frequency signal analysis requiresUse of the analytic signal, and this version, often referred to as theWigner-Ville distribution (WVD), is straightforward to compute, does not exhibit any aliasing problem, and introduces no frequency artifacts.
Abstract: It is shown that a correct use of the Wigner distribution (WD) for time-frequency signal analysis requires use of the analytic signal. This version, often referred to as the Wigner-Ville distribution (WVD), is straightforward to compute, does not exhibit any aliasing problem, and introduces no frequency artifacts. The problems introduced by the use of the Wigner distribution with a real signal are clarified. >
224 citations
23 Feb 1988
TL;DR: In this article, the authors consider instantaneous frequency and its variance using the bilinear joint time-frequency distribu-tions and derive the corresponding quantities for the short-time Fourier spectrum and show the relation to and consistency with the above definition.
Abstract: We consider instantaneous frequency and its variance using the bilinear joint time-frequency distribu-tions. It is well known that these distributions give the instantaneous frequency as the time derivative of the phase. We show that they also lead to a reasonable definition for the standard deviation of instantaneous frequency, namely σw2(t) )= ((A'(t))/(A(t)))2 where A(t) is the amplitude of the signal. We demonstrate the relationship with the bandwidth of the spectrum. We also derive the corresponding quantities for the short-time Fourier spectrum and show the relation to and consistency with the above definition. The concept of local spread of frequencies is used to define and clarify the meaning of multicomponent signals. It is argued that the breaking up of a signal into components is a local phenomenon and that the criteria for a meaningful decomposition is that the standard deviations of instantaneous frequency of each part about their own individual instantaneous frequencies be well separated and small in comparison to the standard deviations of the signal. In addition, we consider the new distributions of Choi and Williams which dramatically enhance the interpretive value and use of bilinear distributions. These distributions suppress the interference terms while preserving the desirable characteristics of the distributions. This is particularly the case for multicomponent signals. We show that if a class of distributions yields a certain expectation value, then the cross terms of the different distributions within that class contribute the identical value towards expectation values. Hence, even though the cross terms may be reduced, they none the less contribute an identical amount towards an expectation value.
110 citations
11 Apr 1988
TL;DR: In this article, 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. >
50 citations
21 Jan 1988
TL;DR: Time-Frequency analysis based on the Wigner-Ville Distribution (WVD) is shown to be optimal for a class of signals where the variation of instantaneous frequency is the dominant characteristic.
Abstract: Time-Frequency analysis based on the Wigner-Ville Distribution (WVD) is shown to be optimal for a class of signals where the variation of instantaneous frequency is the dominant characteristic. Spectral resolution and instantaneous frequency tracking is substantially improved by using a Modified WVD (MWVD) based on an Autoregressive spectral estimator. Enhanced signal-to-noise ratio may be achieved by using 2D windowing in the Time-Frequency domain. The WVD provides a tool for deriving descriptors of signals which highlight their FM characteristics. These descriptors may be used for pattern recognition and data clustering using the methods presented in this paper.
25 citations
23 Feb 1988
TL;DR: In this paper, the problem of choosing a method for time-frequency signal analysis is discussed and a natural approach leads to the introduction of the concepts of the analytic signal and instantaneous frequency, and it is shown that an accurate Time-Frequency representation of a signal can be obtained by using the Wigner-Ville distribution (WVD) for the analysis of a class of signals referred to as "asymptotic" signals.
Abstract: In this paper, the problem of choosing a method for time-frequency signal analysis is discussed. It is shown that a natural approach leads to the introduction of the concepts of the analytic signal and instantaneous frequency. The Wigner-Ville Distribution (WVD) is a method of analysis based upon these concepts and it is shown that an accurate Time-Frequency representation of a signal can be obtained by using the WVD for the analysis of a class of signals referred to as “asymptotic”. For this class of signals, the instantaneous frequency describes an important physical parameter characteristic of the process under investigation. The WVD procedure for signal analysis and synthesis is outlined and its properties are reviewed for deterministic and random signals.
19 citations
11 Apr 1988
TL;DR: The WVD and the cross Wigner-Ville distribution are applied to signal detection and classification, and signal-to-noise ratio (SNR) performance is discussed.
Abstract: The Wigner-Ville distribution (WVD) and the cross Wigner-Ville distribution (XWVD) are applied to signal detection and classification, and signal-to-noise ratio (SNR) performance is discussed. The method is applied to signaturing the individual cylinders of a diesel engine. A comparison with the short-time Fourier transform is provided. >
14 citations
11 Apr 1988
TL;DR: Two signal synthesis algorithms for pseudo-Wigner distribution are presented, the pseudopower method which allows optimal signal synthesis, but is computationally expensive for longer signals, and the partial sum method which is suboptimal but suited for the synthesis of signals with arbitrary length.
Abstract: The pseudo-Wigner distribution (PWD) is a time-frequency signal representation particularly suited for analyzing and processing 'long' signals. Signal processing by means of PWD involves a signal synthesis step. Two signal synthesis algorithms for PWD are presented. These are the pseudopower method which allows optimal signal synthesis, but is computationally expensive for longer signals, and the partial sum method, which is suboptimal but suited for the synthesis of signals with arbitrary length. The performance of the two algorithms is demonstrated by simple synthesis experiments. >
12 citations
11 Apr 1988
TL;DR: The authors present a new method for time scaling of speech signals based on scaling the short-time Fourier transform (STFT) along the time axis while keeping it unchanged along the frequency axis.
Abstract: The authors present a new method for time scaling of speech signals based on scaling the short-time Fourier transform (STFT) along the time axis while keeping it unchanged along the frequency axis. Because the resultant time-frequency function is not an admissible STFT, they project it on the space of admissible STFTs, i.e., they find a signal whose STFT best approximates the time-frequency function. The time-scaled signal is related to the original signal by a linear periodically-time-varying filter, which is simple to implement. High quality time-scaled words and sentences have been obtained using this method. >
5 citations
TL;DR: A class of kernels of short duration is developed for interpolating band-limited signals, and utilizes the rapid attenuation of their Fourier transform based on a minimax mean-square error criterion.
Abstract: A class of kernels of short duration is developed for interpolating band-limited signals. The class consists of modulated splines, and utilizes the rapid attenuation of their Fourier transform. The design is based on a minimax mean-square error criterion. >
4 citations
TL;DR: In this paper, the smoothed pseudo-Wigner distribution was used for the analysis of nonstationary broadband signals, a voiced speech signal, and a flute signal.
Abstract: Several nonstationary broadband signals, a voiced speech signal, and flute signals are studied with the short time Fourier transform (STFT) and the smoothed pseudo‐Wigner distribution. The time frequency description of flute signals is more precise with the smoothed pseudo‐Wigner distribution, and the instant of glottal closure can be reached with better precision in the voiced speech signal. The smoothed pseudo‐Wigner distribution is more suitable for these signals than the STFT.
3 citations
01 Jan 1988
TL;DR: The time-delay estimation algorithrn is presented together with simulation results that show the performance of the technique in the estimation of tirrie-varying delay.
Abstract: A new approach is proposed and investigated for the high resolution estimation and tracking of non-stationary time delay between frequency modulated signals. The method, based on cross-correlation of the pseudo-Wigner Distributions of the noise-contaminated f.m. signals exploits the tirne-varyingo instantaneous fre- quency characteristic of such signals. The time-delay estimation algorithrn is presented together with simulation results that show the performance of the technique in the estimation of tirrie-varying delay.