Showing papers on "Time–frequency analysis published in 1987"

An efficient real-time implementation of the Wigner-Ville distribution

Abstract: The Wigner-Ville distribution (WVD) is a valuable tool for time-frequency signal analysis. In order to implement the WVD in real time, an efficient algorithm and architecture have been developed which may be implemented with commercial components. This algorithm successively computes the analytic signal corresponding to the input signal, forms a weighted kernel function, and analyzes the kernel via a discrete Fourier transform (DFT). To evaluate the analytic signal required by the algorithm, it is shown that the time domain definition implemented as a finite impulse response (FIR) filter is practical and more efficient than the frequency domain definition of the analytic signal. The windowed resolution of the WVD in the frequency domain is shown to be similar to the resolution of a windowed Fourier transform. A real-time signal processor has been designed for evalution of the WVD analysis system. The system is easily paralleled and can be configured to meet a variety of frequency and time resolutions. The arithmetic unit is based on a pair of high-speed VLSI floating-point multiplier and adder chips.

A high resolution data-adaptive time-frequency representation

Abstract: We present a data-adaptive time-frequency representation that obtains high resolution of signal components in time-frequency. This representation overcomes the often poor resolution of the traditional short-time Fourier transform, while avoiding the nonlinearities that make the Wigner distribution and other bilinear representations difficult to interpret and use. The new method uses adaptive Gaussian windows, with the window parameters varying at different time-frequency locations to maximize the local signal concentration in time-frequency. Two methods for selecting the Gaussian parameters are presented: a parameter estimation approach, and a method that maximizes a measure of local signal concentration.

Time-frequency window leakage in the short-time Fourier transform

Abstract: Conventional frequency-domain window-leakage analysis accurately describes the leakage in the short-time Fourier transform only for stationary signals. Leakage in the time-frequency plane from concentrated transient or nonstationary signals can be effectively analyzed by use of a time-frequency window-leakage envelope with rectangular contours. This envelope is obtained from the Wigner distribution of the analysis window, with appropriate corrections for the sidelobe leakage. The time-frequency window-leakage envelope gives insight into the tradeoffs in time-frequency leakage between various windows and allows quick and accurate estimates of the leakage in the short-time Fourier transform. A simple technique for constructing signals with Wigner distributions that are linear transformations of the Wigner distribution of a known signal is developed. With this technique, windows with a variety of time-frequency orientations and leakage behavior can be developed.

Autoregressive modeling of the Wigner spectrum

Abstract: Autoregressive(AR) or linear predictive(LP) modeling and Wigner time-frequency representations have been proposed for non-stationary signal analysis and synthesis, owing to their specific advantages over the short-time Fourier transform, viz. reduced data set characterisation and improved frequency resolution of the former, and the improved time resolution and thence better non-stationary signal representation of the latter. However, the former is limited in time resolution and the latter in frequency resolution and size of characterising data set, depending on the size of the windows that need to be used. This paper investigates the potential combination of the two above methods, with the aim of exploiting their advantages simultaneously and addressing the window size-resolution dilemma. The concept shows good promise to this end, despite the problems of the cross-spectral components and computational complexity, that need to be addressed. Examples of simulated signals are presented to illustrate the advantages of this representation.

Reconstruction from Fourier transform phase with applications to speech analysis

Abstract: This paper addresses the problem of signal reconstruction from Fourier transform phase. In particular, we examine two aspects of this problem. First, we discuss signal reconstruction from the phase spectrum of the short-time Fourier transform(STFT). Next, we examine the problem of signal recovery from partial phase information. We present the results of our studies on reconstruction from partial phase and discuss the application of these results in speech analysis and coding.

Time-varying signals analysis using squared analytic signals

Abstract: Wigner distribution (WD) can provide for high frequency- or time- resolution, but its nonlinear property poses problems when applied to signals with multiple frequency components. This paper proposes an alternative to WD with improved performance for such signals, based on a consideration why WD offers high resolution. The observed data is first converted to analytic signals, which are then subjected to Fourier transform after squaring. Experimental results revealed its superiority over WD for multi-component signals.