A quantitative analysis of SNR in the short-time Fourier transform domain for multicomponent signals

A quantitative analysis is given for the signal-to-noise ratio (SNR) in the short-time Fourier transform domain for multicomponent signals in additive white noise. It is shown that the SNR is increased on the order of O(N/K), where K is the number of components of a signal, N/T is the sampling rate, and T is the window size. The SNR increase rate is optimal for given K. For this result, the SNR definition is generalized, which is suitable for signals not only in the time domain but also in other domains. This theory is illustrated by one numerical example.