Spectral analysis of time varying signals is traditionally performed with the short time Fourier transformation (STFT). In the last few years, many authors have advocated the use of time frequency distributions for this task. This paper has 2 main aims. The first is to reformulate Cohen-class of time frequency representations (TFRs) into discrete-time, discrete-frequency, computer-implemented form. The second aim is to show how, in this form, many of the properties of the continuous-time, continuous-frequency formulation are either lost or altered. Intuitions applicable in the continuous-time case examined here. The properties of the discrete variable formulation examined are the presence and form of cross-terms, instantaneous frequency (IF) estimation and relations between Cohen\u27s class TFRs. We define a parameterized class of distributions which is a blending between the STFT and wigner ville distribution (WVD). The two main conclusions to be drawn are that all TFRs of Cohen\u27s class implementable in the form (which includes all commonly used TFRs) posses cross terms and that IF estimation using periodic moments of these TFRs is purposeless, since simpler methods obtain the same results.
展开▼
