Short-time Fourier analysis tecniques for FIR system identification and power spectrum estimation

Abstract

A wide variety of methods have been proposed for system modeling and identification. To date, the most successful of these methods have been time domain procedures such as least squares analysis, or linear prediction (ARMA models). Although spectral techniques have been proposed for spectral estimation and system identification, the resulting spectral and system estimates have always been strongly affected by the analysis window (biased estimates), thereby reducing the potential applications of this class of techniques. In this paper we propose a novel short-time Fourier transform analysis technique in which the influences of the window on a spectral estimate can essentially be removed entirely (an unbiased estimator) by linearly combining biased estimates. As a result, section (FFT) lengths for analysis can be made as small as possible, thereby increasing the speed of the algorithm without sacrificing accuracy. The proposed algorithm has the important property that as the number of samples used in the estimate increases, the solution quickly approaches the least squares (theoretically optimum) solution. The method also uses a fixed Fourier transform length independent of the amount of data being analyzed, allowing the estimate to be recursively updated as more data is made available. The method assumes that the system is a finite impulse response (FIR) system.