Measures, performance assessment, and enhancement of TFDs

Abstract

This chapter describes a number of time-frequency (t,f) performance quality measures specifically developed as criteria for performance enhancement for a given application. The adopted performance measures are defined using objective criteria followed by time-frequency distribution (TFD) enhancement methods to improve the (t,f) concentration, resolution, and readability of TFDs. The topic is covered in nine articles.

Hyperbolic FM signals are well described by a method related to time-scale analysis and the wavelet transform (Section 7.1). A general procedure for enhancing the time-frequency resolution and readability of TFDs is the reassignment principle described in Section 7.2. Techniques for measuring the concentration of TFDs and for automatic optimization of their parameters are presented based on entropy measures (Section 7.3). Another approach defines a resolution performance measure using local measurements in the (t,f) domain, such as relative amplitudes of auto-terms and cross-terms (Section 7.4). Then, attempts to unify time-frequency, time-scale, filter banks, wavelets, and the discrete-time Gabor transform using product functions and cascaded frames are presented briefly as they may assist in the selection of the best-performing method for a given application (Section 7.5). The last four topics focus on (1) time-frequency compressive sensing (Section 7.6); (2) signal complexity estimation using (t,f) entropy measures (Section 7.7); (3) time-frequency analysis using neural networks (Section 7.8); and (4) a comparison of postprocessing methods in the (t,f) domain (Section 7.9).