ON INSTANTANEOUS AMPLITUDE AND PHASE OF SIGNALS

In many questions of signal processing, it is important to use the con cepts of instantaneous amplitude or phase of signals. This is especial ly the case in communication systems with amplitude or frequency modul ation. These concepts are often introduced empirically. However, it is well known that the correct approach for this purpose is to use the c oncept of analytic signal. Starting from this point, we show some exam ples of contradictions appearing when using other definitions of insta ntaneous amplitude or frequency that are commonly admitted. This intro duces the problem of characterizing pure amplitude-modulated or pure p hase-modulated signals. It is especially shown that whereas amplitude modulated signals can be characterized by spectral considerations, thi s is no longer the case for phase-modulated signals. Furthermore, sign als with constant amplitude have very specific properties, which are a nalyzed in detail. Some consequences and extensions to random signals are finally discussed.