Gradient techniques for voiced/unvoiced speech signal representation using mixed transforms

A technique is proposed for signal representation using partial sets of different transforms which are not, in general, orthogonal with respect to each other. First, the residual error, which is the difference between the original signal and the reconstructed signal, is properly formulated. Then, two gradient techniques are developed to minimize this error and maximize the signal-to-noise ratio of the reconstructed signal using a given total number of transform components in the constrained representation. Sample results using this approach for representing speech signals employing the mixed Fourier/Walsh and Fourier/Haar are given to illustrate the accuracy and effectiveness of the technique