Theoretical Complex Cepstrum of DCT and Warped DCT Filters

In this letter, we derive the theoretical complex cepstrum (TCC) of the discrete cosine transform (DCT) and warped DCT (WDCT) filters. Using these derivations, we intend to develop an analytic model of the warped discrete cosine transform cepstrum (WDCTC), which was recently introduced as a speech processing feature. In our derivation, we start with the filter bank structure for the DCT, where each basis is represented by a finite impulse response (FIR) filter. The WDCT filter bank is obtained by substituting z^-1 in the DCT filter bank with a first-order all-pass filter. Using the filter bank structures, we first derive the transfer functions for the DCT and WDCT, and subsequently, the TCC for each filter is computed. We analyze the DCT and WDCT filter transfer functions and the TCC by illustrating the corresponding pole-zero maps and cepstral sequences. Moreover, we also use the derived TCC expressions to compute the cepstral sequence for a synthetic vowel /aa/ where the observations on the theoretical cepstrum corroborate well with our practical findings