DCT-Based Gabor Transform for Long or Infinite Sequences

The length of discrete signals could be very long in many real applications. In such case, the existing DCT-based real-valued discrete Gabor transform (RGDT) for finite sequences is no longer adequate. In this paper, the novel DCT-based RGDT for infinite sequences is defined and the biorthogonality relationship between the analysis window and the synthesis window for the novel transform is also provided. Because the novel transform only involves real operations and can utilize fast DCT and IDCT algorithms for fast computation, it is easier in computation and implementation by hardware or software as compared to the traditional complex-valued discrete Gabor transform.