Nonuniform Discrete Short-Time Fourier Transform A Goertzel Filter Bank versus a FIR Filtering Approach

Abstract

It is well known that the discrete Short Time Fourier Transform (STFT) can be considered from the perspective of a Discrete Fourier Transform (DFT) taken over short time sections of the signal (the window is fixed) or from the perspective of a filtering operation at a given frequency (the frequency is fixed). We have proposed a mixed approach where the spectrum of each finite short time section of the signal is estimated by realizing a DFT through a bank of IIR Goertzel Filters centered at the specified frequencies. This approach allows computing the time varying spectrum at precisely the frequencies of interest. The Goertzel algorithm can be adjusted to implement the Nonuniform Discrete Fourier Transform (NDFT). Within the NDFT framework the estimation of the spectrum at the desired frequency it is not conditioned to the requirement that the DFT index, k, be an integer. We have termed this implementation of the discrete STFT the "Nonuniform Discrete Short Time Fourier Transform" (NSTFT). A MATLAB program was written and validated using this technique, then the methods were compared for different windows size and different number of frequencies of interest, to a MATLAB FIR filtering view implementation.