Different approximate cepstra using subband-transforms: Theory and applications

Cepstrum analysis is a nonlinear signal-processing method with a variety of applications in areas such as speech, image, and seismic signal processing. The idea of the subband- transforms (the subband-DFT (SB-DFT) and the subband-DCT (SB-DCT)) is to decompose the input signal into low- and high- frequency bands, and then to process the two bands separately after down-sampling. Approximation can be done if it is known that the energy is concentrated in one of the bands. So only this band is calculated resulting in an approximate transform with less computational complexity. In this work the idea of both subband transforms is reviewed. Both transforms are used in cepstrum computation. The SB-DFT cepstrum and the SB-DCT cepstrum are compared in terms of their computational complexity and efficiency with respect to the full- band DFT and full-band DCT cepstra. In many speech processing applications, the DFT-based cepstrum is used to determine the mode of excitation of the model (voiced or unvoiced) and, for voiced speech, the pitch period. In this work the approximated subband-DFT (SB-DFT) is used instead of the full-band DFT (or FFT) to determine both the real cepstrum (called also simply the cepstrum) and the complex cepstrum. It is shown that using the approximate SB-DFT in speech applications does not degrade the information contained in the cepstrum while the computational complexity is highly reduced. The approximated complex cepstrum is used in the problem of echo detection. The adaptive capability of the SB-DFT is included in both SB-DFT cepstrum and SB-DCT cepstrum to adaptively detect the echo for different input frequency bands. Complexity and efficiency of echo detection algorithms based on SB-DFT and SB- DCT cepstra are compared.