Vector-valued time-frequency representations (original) (raw)

The use of a filter bank and the Wigner-Ville distribution for time-frequency representation

IEEE Transactions on Signal Processing, 1999

We present a new method for time-frequency representation, which combines a filter bank and the Wigner-Ville distribution (WVD). The filter bank decomposes a multicomponent signal into a number of single component signals before the WVD is applied. Cross-terms as well as noise are reduced significantly, whereas high time-frequency concentration is attained. Properties of the proposed time-frequency distribution (TFD) are investigated, and the requirements for the filter bank to fulfil these are given. The ability of the proposed non-Cohen's class TFD to reduce cross-terms as well as noise as well as its ability to approximately reconstruct signals are illustrated by examples. The results are compared with those from WVD, the Choi-Williams distribution (CWD), and spectrogram.

Kernel decomposition of time-frequency distributions

IEEE Transactions on Signal Processing, 1994

Bilinear time-frequency distributions (TFD's) offer improved tim+frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In this paper, we introduce some new tools for the interpretation and quantitative comparison of high-resolution TFD's. These tools are used in related work to define lowcost high-resolution TFD's and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFD's. First, each real-_valued TFD is associated with a self-adjoint linear operator $. The spectral representation of 4 expresses the TFD as a weighted sum of spectrograms (SP's). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFD's due to the fact that 4) is not positive.

Signal Synthesis in a Time-Frequency Domain Using the Wigner-Ville Distribution

Time-Varying filtering using the Discreate Wigner-VIIIe Distribution (DWVD) is examined. DWVD signal synthesis algorithms, used to obtain a signal from Its DWVD, are reviewed. Improvements to existing algoirthms are Introduced, giving a reduction In computational load of approximately 50%. Examples of applications such as Improvement of Signal-Noise ratio of a known signal and signal separation are given.

High-Resolution Time-Frequency Signal Analysis by Parametric Modelling of the Wigner-Ville Distribution

sUMMARy We present a technique for high resolution time-frequency signal analysis based on a modified version of the Wigner-Ville Distribution (WVD). This is achieved by recognizing that the WVD is the Fourier Transform of a bilinear complex kernel and replacing the Fourier Transform by a high resolution model based spectral estimator. Singular value decomposition methods are employed to produce spectral estimates which are more robust to noise and less sensitive to model order. The results show that the modified WVD can improve both spectral resolution and tracking of instantaneous frequency.

A high-resolution quadratic time-frequency distribution for multicomponent signals analysis

IEEE Transactions on Signal Processing, 2001

Abstract The paper introduces a new kernel for the design of a high resolution time-frequency distribution (TFD). We show that this distribution can solve problems that the Wigner-Ville distribution (WVD) or the spectrogram cannot. In particular, the proposed distribution can resolve two close signals in the time-frequency domain that the two other distributions cannot. Moreover, we show that the proposed distribution is more accurate than the WVD and the spectrogram in the estimation of the instantaneous frequency of a ...

An analysis of instantaneous frequency representation using time-frequency distributions-generalized Wigner distribution

IEEE Transactions on Signal Processing, 1995

This paper presents an analysis of the representation of instantaneous frequency using time-frequency distributions of energy density domain. Similarity to the "ideal" instantaneous frequency presentation is chosen as a criterion for comparison of various distributions. Although all the commonly used distributions suffer from the artifacts along frequency axis, it is shown that the Wigner distribution is the best among them, with respect to this criterion. The generalization of Wigner distribution-LWD is introduced to decrease the artifacts. The properties of the LWD are analyzed. It is shown that, at the expense of an insignificant increase in computation time, much better results are obtained. The theory is illustrated by a numerical example with the frequency modulated signals.

Short-time fourier transform: two fundamental properties and an optimal implementation

IEEE Transactions on Signal Processing, 2003

Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.

A quantitative comparison of non-parametric time-frequency representations

2005

ABSTRACT In this paper we compare a variety of non-parametric time-frequency methods to determine the best time–frequency representation (TFR) for a collection of signals. These methods include quadratic time-frequency transforms, atomic decomposition and adaptive quadratic time-frequency transforms. The performance measures used to assess the TFRs include; two–dimensional correlation, IF correlation and time-frequency resolution.

A resolution comparison of several time-frequency representations

IEEE Transactions on Signal Processing, 1992

Two signal components are considered "resolved" in a time-frequency representation when two distinct peaks can be observed. The time-frequency resolution limit of two Gaussian components, alike except for their time and frequency centers, are determined for the Wigner distribution, the pseudo-Wigner distribution, the smoothed Wigner distribution, the squared magnitude of the short-time Fourier transform, and the Choi-Williams distribution. The relative performance of the various distributions depends on the signal. The pseudo-Wigner distribution is best for signals of this class with only one frequency component at any one time, the Choi-Williams distribution is most attractive for signals in which all components have constant frequency content, and the matched filter short-time Fourier transform is best for signal components with significant frequency modulation. A relationship between the short-time Fourier transform and the cross-Wigner distribution is used to argue that, with a properly chosen window, the short-time Fourier transform or the cross-Wigner distribution must provide better signal component separation than the Wigner distribution.