Efficient STFT analysis over limited frequency regions
Paneras, Demetrios E
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We address the problem of efficiently computing, over narrow frequency bands, the short-time Fourier transform (STFT) and approximations to the STFT. This problem is important for the design of signal understanding systems that have to efficiently carry out STFT reprocessing of signals in order to examine detailed features of signal components that have already been located within narrow frequency bands. In the computation of the exact STFT we use an "overlap pruning" approach (Covell et al. 1992) for exploiting the commonality of computations between successive slices of the STFT with unity decimation interval. We have also extended this approach to the STFT with non-unity decimation intervals and combined it with a frequency pruning method (Sreenivas et al. 1980) to provide additional computational savings. In the computation of approximations to the STFT we use an algorithm (Khan et al. 1988) for efficiently computing Taylor series approximations over narrow frequency bands. Through examples involving real data we demonstrate the feasibility of using the approximated STFT to obtain more accurate estimates of the center frequency of spectral peaks, and to resolve multiple peaks that have been smeared due to the use of short window lengths. The efficiency of all the algorithms we have investigated is less than 0(N log N) multiplications per STFT slice and can be as small as O(N) multiplications per STFT slice in certain cases. Consequently, all the algorithms compare favourably with the standard FFT implementation of the STFT which requires O(N log N) multiplications per slice. All the algorithms considered in this thesis were implemented in software and tested on synthetic and real sound signals.
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