Multirate Filtering Based Fast Parallel Algorithm For Real-valued Discrete Gabor Expansion And Transform

In 1946, Dennis Gabor presented the Gabor transform, which is useful for non-stationary signal processing. It overcomes the problem that the traditional Fourier transform can not used to explain how the frequency components of a signal change with time. The coefficients of Gabor transform can reveal the local frequency information of a signal or an image, which has been proved to be useful for signal and image processing in various fields such as time and frequency analysis, image understanding, texture analysis, image division and pattern recognition. Its real time applications, however, were limited due to the high computational complexity of the Gabor transform algorithms.For the above reasons, the real-valued discrete Gabor transform (RDGT) with the kernel of the discrete Hartley transform (DHT) was proposed by Liang Tao, et al. Compared with the traditional complex-valued discrete Gabor transform (CDGT), it involves only the real-valued computation, and can utilize the fast DHT algorithm to speed up the transform, so the computation load of the discrete Gabor transform and expansion can be greatly reduced. And consequently, the implementation of the RDGT can be made easier by hardware and software.In order to implement the DHT kernel-based RDGT even faster, this thesis presents a multirate filtering based fast parallel algorithm for the RDGT and its inverse transform. In the algorithm, an analysis filter bank will be designed for the RDGT and a synthesis filter bank will be designed for the inverse RDGT (i.e., real-valued discrete Gabor expansion). Each of the parallel channels in the two filter banks has a unified structure and can apply the fast DHT algorithm to reduce its computational load. The computational complexity related to computational time of the proposed parallel algorithm is analyzed and compared with that of the existing parallel algorithms. The results indicate that the proposed parallel algorithm for the DHT kernel-based RDGT and its inverse transform is very attractive for real time signal processing.