On relationships between amplitude and phase of short-time Fourier transform

摘要

The relationships between the amplitude and phase of the short-time Fourier transform (STFT) are investigated. By choosing the Gaussian window for the STFT, we reveal that the group delay and instantaneous frequency of each signal segment, both of which are derived from the phase by definition, can also be explicitly linked with the amplitude. As a result, the amplitude and phase can also be linked through the group delay or instantaneous frequency without making any assumptions for the phase property of the target signals, e.g., minimum, maximum, or linear phase. The theoretical basis is also confirmed in numerical simulations.