New Results On Multiple Correlations

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Abstract
Standard approaches to linear prediction, parameter estima- tion, system identification, and classification problems, involve the autocorrelation sequence of a deterministic, or, stochastic signal or system. This paper presents preliminary results on the same 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. Com- bining second- and higher-order correlations a mean-square parameter estimator is found to have smaller error than the autocorrelation-based estimator. By exploiting the redun- dancy present in multiple correlations a frequency-domain algorithm is developed and applied to reconstruction of noisy signals, and identification of systems from input and output data that are contaminated by colored Gaussian noise of unknown covariance. Finally, under the same noise condi- tions, a noise-resistant matched filter classifier is described.

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