Unified parallel lattice structure of block time-recursive real-valued discrete Gabor transforms

In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in our previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are developed in both the critical sampling case and the oversampling case. Unified parallel lattice structures for the implementation of the algorithms are studied. Also the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach for the computation of the discrete Gabor transforms