One or Two Ridges? An Exact Mode Separation Condition for the Gabor Transform

In this paper, we investigate the conditions for the separation of two pure tones from the spectrogram computed with a Gaussian window. For this purpose, we put forward necessary and sufficient conditions for the existence of spectrogram ridges associated with each signal. We then show how this condition easily extends to the case of parallel linear chirps, i.e., signals with constant amplitude, linear instantaneous frequency, and same chirp rate.