Showing papers on "Time–frequency analysis published in 1996"

Joint time-frequency analysis : methods and applications

Abstract: Classical Signal Analysis. Signal Joint-Time Frequency Representations. Wigner-Ville Distribution. Time-Frequency Distribution Series. Adaptive Gabor Expansion and Adaptive Spectrogram. Applications of JFTA. Instantaneous Frequency Estimation. Time-Varying Signal Pattern Recognition and Classification. Non-Linear Time-Varying Filtering.

Selective discrete Fourier transform algorithm for time-frequency analysis: method and application on simulated and cardiovascular signals

Abstract: The Selective Discrete Fourier transform (DFT) Algorithm [SDA] method for the calculation and display of time-frequency distribution has been developed and validated. For each time and frequency, the algorithm selects the shortest required trace length and calculates the corresponding spectral component by means of DFT. This approach can be extended to any cardiovascular related signal and provides time-dependent power spectra which are intuitively easy to consider, due to their close relation to the classical spectral analysis approach. The optimal parameters of the SDA for cardiovascular-like signals were chosen. The SDA perform standard spectral analysis on stationary simulated signals as well as reliably detect abrupt changes in the frequency content of nonstationary signals. The SDA applied during a stimulated respiration experiment, accurately; detected the changes in the frequency location and amplitude of the respiratory peak in the heart rate (HR) spectrum. It also detected and quantified the expected increase in vagal tone during vagal stimuli. Furthermore, the HR time-dependent power spectrum displayed the increase in sympathetic activity and the vagal withdrawal on standing. Such transient changes in HR control would have been smeared out by standard heart rate variability (HRV), which requires consideration of long trace lengths. The SDA provides a reliable tool for the evaluation and quantification of the control exerted by the Central Nervous System, during clinical and experimental procedures resulting in nonstationary signals.

Analysis of nonlinear FM signals by pattern recognition of their time-frequency representation

Abstract: The aim is to propose a method for detection and parameter estimation of nonlinear FM signals, mono- or multicomponent, embedded in white Gaussian noise. The proposed approach consists in mapping the signal into the time-frequency plane by a time-frequency distribution with reassignment, and then in applying a pattern recognition technique, like the Hough transform, to the time-frequency representation to recognize specific shapes. The advantages of this method over the conventional maximum likelihood estimator are (1) a simpler implementation, because it reduces the dimension of the search space and (2) a consistent attenuation of the interference terms between different components of a signal or between signal and noise.

Time-frequency analysis of musical signals

Abstract: The major time and frequency analysis methods that have been applied to music processing are traced and application areas described. Techniques are examined in the context of Cohen's class, facilitating comparison and the design of new approaches. A trumpet example illustrates most techniques. The impact of different analysis methods on pitch and timbre examination is shown. Analyses spanning Fourier series and transform, pitch synchronous analysis, heterodyne filter, short-time Fourier transform (STFT), phase vocoder, constant-Q and wavelet transforms, the Wigner (1932) distribution, and the modal distribution are all covered. The limitations of windowing methods and their reliance on steady-state assumptions and infinite duration sinusoids to define frequency and amplitude are detailed. The Wigner distribution, in contrast, uses the analytic signal to define instantaneous frequency and power parameters. The modal distribution is shown to be a linear transformation of the Wigner distribution optimized for estimating those parameters for a musical signal model. Application areas consider analysis, resynthesis, transcription, and visualization. The more stringent requirements for time-frequency (TF) distributions in these applications are compared with the weaker requirements found in speech analysis and highlight the need for further theoretical research.

A new procedure for detecting nonlinearity from transient data using the gabor transform

Abstract: A new technique for the identification of nonlinearity in multi-degree of freedom systems is presented. The technique is based on the joint application of the Gabor and the Hilbert transforms to the transient response of a system. The Gabor transform is used first to identify a time-variant matrix representing the spatial behaviour of the system. This matrix is then used to decouple the transient response into a set of uncoupled quasi-harmonic components. Finally the Hilbert transform is applied to identify the dissipative and restoring forces associated with each component which is equivalent to a single degree of freedom system. Numerical examples are supplied to help clarify the main advantages and the possible limitations of the method in the presence of strong nonlinearities and closely spaced frequencies.

Advances in time-frequency analysis of biomedical signals.

Abstract: The frequency content of many biomedical signals can change rapidly with time. Conventional Fourier spectral analysis techniques are insufficient for analyzing the time-varying spectral content of these signals. By mapping a one-dimensional function of time (or frequency), the time-frequency representation can localize the signal energy in both the time and frequency directions. It has been shown that many biomedical signal problems may benefit from time-frequency analysis. The objective of this paper is to review the advances in time-frequency analysis of biomedical signals. Relevant theoretical methodologies and practical considerations are introduced, and five application areas are reviewed: electroencephalography (EEG), electrocardiography, phonocardiography, electrogastrography, and electromyography.

Wigner-based formulation of the chirplet transform

Abstract: Using the Wigner distribution, we derive and analyze a matrix formulation for the chirplet transform, a signal analysis tool that generalizes the wavelet and short-time Fourier transforms. The formulation expresses the translations, scalings, and shears of the chirplet transform in terms of affine matrix transformations on the time-frequency plane. Our approach leads naturally to several new signal transforms, which we derive, analyze, and extend.

Time-frequency analysis of electroencephalogram series. II. Gabor and wavelet transforms.

Abstract: In this paper we compare two methods, based on the Gabor and wavelet transforms, to quantify and visualize the time evolution of frequency contents of electroencephalogram (EEG) time series. We found an optimal correlation between EEG visual inspection and the proposed methods in the characterization of the frequency and energy content of characteristic activity during an epileptic seizure. The quasimonofrequency behavior observed in the epileptic EEG series, in a previous work using a Gabor analysis [J. Inst. Electr. Eng. 93, 429 (1946)], is confirmed with the analysis using a wavelet. Moreover, the method based on the wavelet transform allows us to build a detector of epileptic events. Both methods are exemplified with EEG series obtained with depth electrodes in refractory epileptic patients.

Detection of echoes using time-frequency analysis techniques

Abstract: The following is a presentation of echo detection techniques based on time-frequency signal analysis for the measuring of thickness in thin multilayer structures. These techniques are shown to provide high-resolution signal characterization in a time-frequency space, and good noise rejection performance. In particular, the short-time Fourier transform, the Gabor expansion, the cross-ambiguity function and the Wigner-Ville distribution are analyzed and compared with techniques such as the logarithmic power spectrum, cepstrum and the segmented chirp Z-Transform. A suitable operating procedure was set up, based on an initial emulation phase in which simulated signals were considered, followed by a second phase in which real signals were processed. The results show the optimum performances of these new techniques compared with the traditional ones and, in particular, that the accurate measurement of thickness can be obtained also when waveform transients partially overlap.

Speech analysis and coding using a multi-resolution sinusoidal transform

Abstract: The sinusoidal transform, as developed by Quatieri and McAulay (1986), provides a sparse representation for speech signals by taking advantage of psychoacoustic masking. The currently reported work takes the sinusoidal transform one step further by considering the frequency resolution abilities of the human auditory system in more detail. The new transform is based on the wavelet principle of variable resolution in time/frequency analysis. Specifically, a sinusoidal transform is developed which uses quadrature mirror filter (QMF) banks to obtain better time resolution at high frequencies and better frequency resolution at low frequencies. This naturally provides a perceptually improved allocation of the sinusoids. The new transform matches the human auditory system better than its predecessor and it also matches speech signals well, both fricative sounds and voiced speech. The QMF based ST is then shown to be equivalent to a more efficient FFT based implementation.

Calculating the dual Gabor window for general sampling sets

Abstract: Methods for the calculation of the so-called dual Gabor window for general sampling sets are developed. First, we consider the standard situation where the time-frequency plane (TF-plane) is (over)sampled on a grid, i.e., a rectangular lattice is considered with more points than the dimension of the signal space. Second, we show that the proposed method can be easily extended to general subgroups of the TF-plane. One typical example of such a sampling set is the so called quincunx-lattice.

Precise detection of a P-wave in low S/N signal by using time-frequency representations of a triaxial hodogram

Abstract: We have developed a signal processing technique for three-component microseismic data that allows the precise determination of P-wave arrival times. The method is based on a time-frequency representation of the signal that allows the evaluation of the 3-D particle motion from seismic waves in both time and frequency domains. A spectral matrix is constructed using the time-frequency distributions. A crosscorrelation coefficient for the three-component signal is derived through eigenvalue analysis of the spectral matrix. The P-wave arrival time is determined through a statistical test of hypotheses using the crosscorrelation coefficient. This signal processing method is evaluated using a synthetic signal and it is compared to the local stationary autoregressive method for determining P-wave arrival times. We also show that the proposed method is capable of determining the arrival time of a synthetic P-wave to within 1 ms (five points in the discrete time series) in the presence of a signal-to-noise ratio of -5dB. The method can detect the arrival time of different frequency components of the P-wave, which is a possibility for the evaluation of velocity dispersion of the seismic wave. We demonstrate the feasibility of the method further by applying it to microseismic data from a geothermal field.

Transient analysis on machinery condition monitoring

Abstract: In this research, three main time-frequency/time-scale (TF/TS) analysis algorithms-windowed Fourier transform (WFT), Wigner-Ville distribution (WVD), and wavelet analysis (WA), have been studied and implemented. We compare the different algorithms using an identical set of synthetic signals, from which one can realize their individual features. To justify the effectiveness and to highlight the requisite of using TF/TS analysis, two test-benches have been conducted and investigated. One is to analyze transient vibration signals measured on the end-effector of an industrial robot during plane motion and the other is to analyse the nonstationary vibration response of a rotor-dynamic system with both an electro-mechanical clutch and brake.

Time-frequency analysis of compressor rotating stall by means of wavelet transform

Abstract: In this paper, an application of Wavelet Transform, which is a newly developed time-frequency technique of signal processing, is demonstrated in analyzing compressor rotating stall signals. In contrast to conventional signal processing methods, e.g. Fourier Transform, Wavelet Transform is very suitable for analyzing transient processes as rotating stall inception in compressors. In this study, some typical rotating stall signals are processed via Morlet’s wavelet. It is concluded that Wavelet Transform has a great advantage in detecting rotating stall inceptions, which are usually very weak and embedded in relatively stronger noises. In the diagrams resulted from the transform, every emergence of precursor as well as full stall signals of a certain frequency is illustrated versus time.Copyright © 1996 by ASME

High-accuracy, low-distortion time-frequency analysis of signals using rotated-window spectrograms

Abstract: A speech processing and analysis apparatus and method for generating a time-frequency distribution of a speech signal combines a set of spectrograms with varying window lengths and orientations to provide a parameter-less time-frequency distribution having good joint time and frequency resolution at all angular orientations. The analysis window of a spectrogram is rotated relative to the frequency components of the signal by preprocessing using a Fractional Fourier Transform to form rotated window spectrograms. In particular, to form the rotated window spectrogram, the signal is initially pre-processed using a Fractional Fourier Transform of angle α, the spectrogram time-frequency distribution of the pre-processed signal is then computed using analysis window h(t) and then rotated by angle -α. The geometric mean of a set of rotated window spectrograms, which are indexed by both the analysis window length and the angular orientation of the window relative to the signal's time-frequency features, is then computed to form a combination of rotated window spectrograms.

A pseudo-Bertrand distribution for time-scale analysis

Abstract: Using the pseudo-Wigner time-frequency distribution as a guide, we derive two new time-scale representations: the pseudo-Bertrand and the smoothed pseudo-Bertrand distributions. Unlike the Bertrand distribution, these representations support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the affine smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components.

Evolutionary spectral analysis using a warped Gabor expansion

Abstract: In this paper, we present a Gabor representation based on a nonrectangular tiling of the time-frequency plane and use it to improve the time and frequency resolutions of evolutionary spectra. In the traditional Gabor expansion, a signal is decomposed into a weighted combination of sinusoidally modulated windows resulting in a rectangular time-frequency plane tiling. Poor time and frequency localizations occur in the evolutionary spectrum when the corresponding signal is not modeled well by this fixed-window analysis. We are thus proposing the warped Gabor representation based on a linear chirp model for the signal. By means of a frequency transformation we are able to use the previous sinusoidal representation and choose the Gabor coefficients according to either a frequency masking or an energy concentration measure. Examples are given to illustrate our procedures.

Optimal quadratic detection and estimation using generalized joint signal representations

Abstract: Time-frequency analysis has significant advances in two main directions: statistically optimized methods that extend the scope of time-frequency-based techniques from merely exploratory data analysis to more quantitative application and generalized joint signal representations that extend time-frequency-based methods to a richer class of nonstationary signals. This paper fuses the two advances by developing optimal detection and estimation techniques based on generalized joint signal representations. By generalizing the statistical methods developed for time-frequency representations to arbitrary joint signal representations, this paper develops a unified theory applicable to a wide variety of problems in nonstationary statistical signal processing.

New approach for blind source separation using time-frequency distributions

Abstract: This paper deals with the problem of blind source separation which consists of recovering a set of signals from instantaneous linear mixture of them. So far, this problem has been solved using statistical information available on the source signals. Here, we propose an approach for blind source separation based on time-frequency (t-f) signal representations. This approach is based on a `joint diagonalization' of a combined set of time frequency distribution matrices which correspond to different t-f points. It relies on the difference in the t-f signatures of the sources to be separated. In contrast to existing techniques, the proposed approach allows the separation of Gaussian sources with identical spectra shape. Because of changes incurred in the t-f signal structures due to time- delay, the new approach can be employed to separate multipath signals received by multi-sensor array. Moreover, the effects of spreading the noise power while localizing the source energy in the time frequency domain amounts to increasing the signal to noise ratio and hence improved performance. Numerical examples are provided to illustrate the effectiveness of our method.

A fast recursive STFT algorithm

Abstract: The short-time Fourier transform (STFT) of a signal maps a one-dimensional signal, into a two-dimensional signal in the time-frequency plane. The combination of time-domain and frequency-domain analysis yields a more revealing picture of the signal, showing which spectral components are presented in the signal at a given time. This paper presents an efficient recursive algorithm to compute multiple-pole window STFT of a discrete-time sequence. It is shown that multiple-pole windows offer good time-frequency resolution and that the resulting STFT does not possess any sidelobes. The algorithm of multiple-pole STFT is then derived. It updates STFT only at each N-th point and enables use of the FFT algorithm for efficient computing. Numerical examples are presented.

Generalized Gabor expansions of discrete-time signals in l/sup 2/(Z) via biorthogonal-like sequences

Abstract: In this paper, a biorthogonal-like sequences (BLS) theory and its application to the generalized Gabor expansions (equivalently, the generalized short-time Fourier transform/filterbank summation) are presented. A pair of BLS's are defined to be two sequences satisfying a biorthogonal-like condition (BLC), which is a moment equation and equivalent to a linear difference equation. We show that two collections in a Hilbert space generated by a pair of BLS's in the joint time-frequency domain are complete, either can be used as an analysis filter, and the other can be used as a synthesis filter for a generalized Gabor expansion of discrete-time signals. A sufficient and necessary condition on the existence of BLS's based on the moment equation is presented, which is simpler to use than frame theory. Given a filter generating a frame, its BLS's also generate frames. The dual frame is one of them. Given a FIR analysis/synthesis filter, there is a FIR synthesis/analysis filter if BLS's exist. The algorithm to compute FIR analysis and synthesis filters based on the linear difference equation is presented in this paper, which is simpler than frame operator.

Wigner-transform implementation in the time-frequency domain.

Abstract: An analogy between two-dimensional space and time optics is presented. A setup that performs the time–frequency Wigner transform is proposed, and as an example the propagation of a Gaussian pulse in such a setup is analyzed.

Parametric estimation of multicomponent signals using minimum cross entropy time-frequency distributions

Abstract: The analysis and representation of multicomponent signals, embedded in additive Gaussian noise, is of interest in many signal processing applications and has been studied for years, mainly for the case of stationary signals. However, in the non-stationary case only a few methods are available, one of which is parameter analysis from the time-frequency distribution (TFD) of the signal. A new positive distribution free of cross-terms, named minimum cross entropy-TFD (MCE-TFD) was introduced previously. Based on this TFD, an algorithm for signal reconstruction from the MCE representation is introduced. The algorithm synthesizes the instantaneous frequency (IF), the phase /spl phi/(t) and the amplitude a(t) of each signal component and thus the entire original signal. Together with the MCE-TFD iterative approach, the proposed reconstruction algorithm provides a powerful tool for the representation and analysis of non-stationary multicomponent signals.

Psychovisually tuned wavelet fingerprint compression

Abstract: We present biorthogonal and orthonormal wavelets for embedded zerotree wavelet compression of fingerprint images. By simulated annealing over the wavelet filter coefficients, using a composite cost function dependent upon a parameter k/sup 2/ which weights the relative importance of the wavelet's bandwidth and time dispersion, a series of wavelets is obtained. Each of these is optimal in terms of a particular Heisenberg uncertainty 'footprint', i.e. a particular trade-off between bandwidth and time dispersion. The psychovisually optimal wavelet for fingerprint image compression is determined by fingerprint experts by examination of images compressed and recovered using the series of wavelets. Psychovisually tuned wavelets were found to yield superior visual fidelity to standard wavelets and also to wavelets optimized to produce minimum RMS error on either fingerprint or general test images.