Fast approximate DCT: basic-idea, error analysis, applications

The discrete cosine transform (DCT) has a variety of applications in image and speech processing. The idea of the subband-DFT (SB-DFT) is applied by Jung, Mitra and Mukherjee (see IEEE Trans. on Circuits and Systems for Video Technology, vol.6, no.3, 1996) to the DCT. In this paper the basic idea of the SB-DCT is discussed which is based on subband decomposition of the input sequence. Approximation is done by discarding the computations of bands of little energy. The complexity of this fast approximate method is examined in comparing it with a fast cosine-transform method in terms of program running-time. New accurate analysis of the errors due to the approximation is presented for any number of decomposition stages. New applications of the SB-DCT in the speech cepstrum analysis and in echo detection are also included by using the SB-DCT instead of the full-band FFT in calculating the real and complex cepstra