A unified approach to the STFT, TFDs, and instantaneous frequency

Cohen's class of time-frequency representations (TFRs) is reformulated into a discrete-time, discrete-frequency, computer-implementable form. It is shown 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 do not necessarily carry over to the discrete-time case examined. The properties of the discrete variable formulation examined are the presence and form of cross-terms, instantaneous frequency estimation, and relationships between Cohen's class of TFRs. A parameterized class of distributions which is a blending between the short-time Fourier transform (STFT) and the Wigner-Ville distribution. The two main conclusions are that all TFRs of Cohen's class implementable in the given form (which includes all commonly used TFRs) possess cross-terms and that instantaneous frequency estimation using periodic moments of these TFRs is purposeless, since simpler methods obtain the same result.<
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