Chapter 3 - Theory of Quadratic TFDs

This chapter discusses the theory of quadratic time frequency distributions (TFDs). For a monocomponent linear FM signal, the Wigner-Ville distributions (WVD) is optimal for energy concentration about the instantaneous frequency (IF) and for unbiased estimation of the IF. If a signal has nonlinear frequency modulation or multiple components, the WVD suffers from inner artifacts or outer artifacts (cross-terms), respectively; in either case, some form of reduced interference quadratic TFD (RID) is to be preferred over the WVD. The design of RIDs is best undertaken by designing the desired kernel filter in the ambiguity domain, and using Fourier transforms to see the effects in the time-lag and time–frequency domains. To be a useful tool for practical applications, quadratic TFDs are expected to be real, to satisfy the global and local energy requirements, and to resolve signal components while reflecting the components' IF laws through the peaks of their dominant ridges in the (t, f) plane.

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