DISCRETE COSINE TRANSFORMS
The Discrete Cosine Transform (DCT) is simply a computationally efficient version of the DFT for signals that are real and even (x(n) = x(N-n)): reduces to: The DCT-II, which is one of two common implementations of the DCT used in speech processing, is defined as: The DFT and DCT are related by the following equations: The forward DCT is used in a speech recognition front end to convert samples of the log magnitude spectrum to cepstral coefficients.