Fast parallel algorithms for discrete Gabor expansion and transform based on multirate filtering

Abstract

The Gabor transform has long been recognized as a very useful tool for the joint time and frequency analysis in signal processing. Its real time applications, however, were limited due to the high computational complexity of the Gabor transform algorithms. In this paper, some novel and fast parallel algorithms for the finite discrete Gabor expansion and transform are presented based on multirate filtering. An analysis filter bank is designed for the finite discrete Gabor transform (DGT) and a synthesis filter bank is designed for the finite discrete Gabor expansion (DGE). Each of the parallel channels in the two filter banks has a unified structure and can apply the FFT and the IFFT to reduce its computational load. The computational complexity of each parallel channel does not change as the oversampling rate increases. In fact, it is very low and depends only on the length of the input discrete signal and the number of the Gabor frequency sampling points. The computational complexity of the proposed parallel algorithms is analyzed and compared with that of the major existing parallel algorithms for the finite DGT and DGE. The results indicate that the proposed parallel algorithms for the finite DGT and DGE based on multirate filtering are very attractive for real time signal processing.