New results on multiple correlations

Standard approaches to linear prediction, parameter estimation, system identification, and classification problems involve the autocorrelation sequence of a deterministic or stochastic signal or system. The author presents preliminary results of these problems using higher than second-order correlations. By optimizing a weighted mean-square prediction error, a linear prediction filter that uses triple correlations is derived and its potential for speech analysis and synthesis is discussed. For enhancing noisy speech, a noise canceler based on triple correlations, is proposed. Combining second and higher order correlations, a mean-square parameter estimator is found to have smaller error than the autocorrelation-based estimator. By exploiting the redundancy present in multiple correlations a frequency-domain algorithm is developed and applied to the reconstruction of noisy signals and the identification of systems from input and output data that are contaminated by colored Gaussian noise of unknown covariance. Finally, under the same noise conditions, a noise-resistant matched filter classifier is described.