Instantaneous bandwidth for signals and spectrogram

The concept of instantaneous bandwidth, which is an indication of the frequency spread at a given time, is developed. It is shown that the global bandwidth of a signal can naturally be broken up into an AM and an FM contribution and that the AM contribution comes from averaging the instantaneous bandwidth. The instantaneous bandwidth for the spectrogram is derived, and series expansions in terms of the derivatives of the phase are obtained.<<ETX>>