Multirate-based fast parallel algorithms for DCT-kernel-based real-valued discrete Gabor transform
Fast parallel algorithms for the DCT-kernel-based real-valued discrete Gabor transform (RDGT) and its inverse transform are presented based on multirate signal processing. An analysis convolver bank is designed for the RDGT and a synthesis convolver bank is designed for its inverse transform. The parallel channels in each of the two convolver banks have a unified structure and can apply the fast DCT algorithms to reduce computation. The computational complexity of each parallel channel is low and depends mainly on the length of the discrete input signal and the number of the Gabor frequency sampling points. Every parallel channel corresponds to one RDGT coefficient, and all the RDGT coefficients are computed in parallel during the analysis process and are finally reconstructed in parallel as pieces of the original signal during the synthesis process. The computational complexity related to the computational time of each RDGT coefficient or each piece of the reconstructed signal in the proposed parallel algorithms is analyzed and compared with those in the existing major parallel algorithms for the RDGT and its inverse transform. The results indicate that the proposed multirate-based fast parallel algorithms for the RDGT are attractive for real-time signal processing.
real-valued discrete gabor transform dct kernel multirate filtering analysis and synthesis convolver banks