On an ambiguity in the definition of the amplitude and phase of a signal

We point out that the conventional definition of instantaneous amplitude an d frequency, namely as the magnitude and derivative of the phase, respectiv ely, of a complex representation of the signal sometimes contains an ambigu ity, even for a unique complex representation (e.g., the analytic signal). There are at least two choices for resolving this ambiguity when it arises. One choice yields a nonnegative amplitude but an instantaneous frequency w ith infinite spikes, and one yields a bounded instantaneous frequency but a n instantaneous amplitude with positive and negative values. Historically, both solutions (i.e., both amplitudes) have been important in radio enginee ring, and both can be measured with real devices. The former choice is more commonly used for defining the instantaneous amplitude and frequency of si gnals, but the latter choice is equally acceptable and may be preferred in some situations. (C) 1999 Elsevier Science B.V. All rights reserved.