DCT-Based Real-Valued Discrete Gabor Transform and Its Fast Algorithms

The traditional DCT-based real-valued discrete Gabor transform (RGDT) was limited to the critical sampling case. The biorthogonality relationship between the analysis window and synthesis window for the transform was not unveiled. To overcome those drawbacks, this paper proposes a novel DCT-based real-valued discrete Gabor transform, which can be applied under both the critical sampling condition and the over-sampling condition, and the biorthogonality relationship between the analysis window and synthesis window for the novel transform can be derived. Because the proposed DCT-based RDGT only involves real operations and can utilize fast DCT algorithms for fast computation, it is easier in computation and implementation by hardware or software compared to the traditional complex-valued discrete Gabor transform.