A method and apparatus for speech recognition using second order statistics and linear estimation of cepstral coefficients. In one embodiment, a speech input signal is received and cepstral features are extracted. An answer is generated using the extracted cepstral features and a fixed signal independent diagonal matrix as the covariance matrix for the cepstral components of the speech input signal and, for example, a hidden Markov model. In another embodiment, a noisy speech input signal is received and a cepstral vector representing a clean speech input signal is generated based on the noisy speech input signal and an explicit linear minimum mean square error cepstral estimator.