Novel DCT-based real-valued discrete Gabor transform

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 the synthesis window for the transform has not been 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 the synthesis window for the transform is also proved in this paper. Because it only involves real operations and can utilize fast DCT and IDCT algorithms for fast computation, it facilitates computation and implementation by hardware and/or software compared to the traditional complex-valued discrete Gabor transform.