Analytic Signal Representation

Chapter 2 treats some basic mathematical properties of the HT, and of the analytic signal, which allow one to determine the amplitude, phase, and frequency of any oscillation at any instant of time. The focus of this chapter is a rigorous derivation of the HT envelope and the instantaneous frequency, including the question of their negative values. The instantaneous frequency always has a simple and clear physical meaning. The negative instantaneous frequency is not “unphysical,” it can be easily understood through the variations in phase angle. A generalized product theorem for HT is presented for operating with overlapping spectra signals.