In this paper, we present a new and robust method, general time-frequency distribution series (TFDS), for time-frequency analysis. We also introduce the concept of local interference and global interference and show that the local interference is important and the global interference is less important in TF analysis. The TFDS is very general. With only one parameter, order of the TFDS, one can ...

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and nonstationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictiona...

We introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions , a matching pursuit deene...

A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal is changing in time, and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic goal is to devise a distribution that represents the energy or intensit...

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...

Efficient measurement of time-frequency distributions (TFDs) concentration can provide a quantitative criterion for evaluation of various distributions performance. It can be used for adaptive and automatic parameter selection in time-frequency analysis, without supervision of a user. Measures for distribution concentration of monocomponent signals date back to [3], [8]. For more complex signal...

2. TIME-FREQUENCY REPRESENTATIONS Many functions have been proposed for estimating signal information content and complexity on the time-frequency plane, including moment-based measures such as the timebandwidth product and the Shannon and RCnyi entropies. When applied to a time-frequency representation from COhen’s class, the R h y i entropy conforms closely to t.he visually based notion of co...