Analysis of an adaptive short-time Fourier transform-based multicomponent signal separation method derived from linear chirp local approximation

Recently, a direct method of the time–frequency approach, called signal separation operator (SSO), which is based on sinusoidal approximation, was introduced to solving inverse problem multicomponent separation. In very recent paper “Direct via extraction local frequencies with adaptive time-varying parameters”, authors obtained more accurate component recovery formula derived from linear chirp (also frequency modulation signal) approximation at any time. However theoretical analysis has not been studied there. this paper, we carry out SSO short-time Fourier transform (STFT). We study both signal-based model and chirp-based model, obtain error bounds for instantaneous estimation recovery. The are by studying STFT each assumption decrease window function STFT. These results provide mathematical guarantee proposed STFT-based non-stationary method. addition, experiments provided illustrate general theory.