Adaptive system identification using time-varying Fourier transform

In this paper, we introduce a time-varying short-time Fourier transform (TV-STFT) for representing discrete signals. We derive an explicit condition for perfect reconstruction using time-varying analysis and synthesis windows. Based on the derived representation, we propose an adaptive algorithm that controls the length of the analysis window to achieve a lower mean-square error (MSE) at each iteration. When compared to the conventional multiplicative transfer function approach with a fixed length analysis window, the resulting algorithm achieves faster convergence without compromising for higher steady state MSE. Experimental results demonstrate the effectiveness of the proposed approach.