General Sub-Band DCT: Fast Approximate Adaptive Algorithm

The discrete cosine transform (DCT) has a variety of applications in image and speech coding [1, 2]. The idea of the approximate subband DFT (SB-DFT) [3, 4] is applied in [5] and [6] to the DCT. In this paper the basic idea of the subband DCT (SB-DCT) is reviewed. The calculation of the approximate SB-DCT is done with the aid of a fast cosine-transform method [7]. The subband DCT is generalized such that any band out of M subbands can be calculated. For this purpose the fast DCT method [7] is modified to calculate the fast DST. A general analysis of the errors due to the approximation is presented. The adaptive capability of the SB-DFT given in [8] is added to the SB-DCT to calculate adaptively the band of the dominant energy. The two-dimensional (2-D) SB-DCT is also investigated in this work. Applications of the general adaptive SB-DCT in speech cepstrum analysis and in echo detection are included. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.