This chapter provides an extended in-depth treatment of the material described in Chapter I. It focuses on the precise description of the key concepts and formulations needed to formally describe time-frequency (t, f) methods. Section 1.1 describes in detail the justifications why time-frequency methods are preferred for a wide range of applications in which the signals have time-varying spectral characteristics or multiple components for which the variables t and f are related. Section 1.2 provides the signal models and mathematical formulations needed to describe temporal and spectral characteristics of nonstationary signals in the time-frequency domain. It defines such basic concepts as analytic signals, Hilbert transform, bandwidth-duration product, and asymptotic signals. Section 1.3 defines the key characteristic quantities related to time-frequency methods, including the instantaneous frequency (IF), spectral delay (SD), and group delay (GD). Section 1.4 reinforces the material in the previous sections with a simple tutorial on defining the AM/FM characteristics of signals using the concepts of analytic signal and IF; and therefore allowing a unique definition of the amplitude and phase of a nonstationary signal.

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