DCT based pseudo complex cepstrum

We propose two algorithms. which effectively use Discrete Cosine Transform (DCT) to obtain complex cepstrum, which we call as the Discrete Cosine Transformed Cepstrum (DCTC). The first algorithm uses the relation between Discrete Fourier Transform (DFI) and DCT II. Computing the complex cepstrum using Fourier Transform needs unwrapped phase. The calculation of the unwrapped phase is sometimes difficult due to the presence of multiple zeros and poles near or on the unit circle. Since DCT is a real function, its phase can only be 0 or π and phase unwrapping is done by representing negative by exp( ∼jπ) and positive by 1. The motivation for the second algorithm is to obtain DCTC by representing DCT sequence itself by magnitude and phase components. Phase unwrapping is performed in the same way as in the case of first algorithm. We tested DCTC by simulating the impulse response of a system that has multiple poles and zeros near or on the unit circle and we have shown that DCTC provides a closer match to the theoretical complex cepstrum than the DFT based complex cepstrum. DCTC has been used to obtain the pitch contour of syllables, words and sentences. It is shown that the first few coefficients' spectral envelope matches with the envelope of the signal spectrum under consideration. We are also exploring the applicability of DCTC to speaker recognition.