Residual error formulation and adaptive minimization for representing nonstationary signals using mixed transforms

A technique is proposed for signal representation using superimposed partial sets of different transforms which are, in general, nonorthogonal to each other. The method is developed to maximize the signal-to-noise ratio (SNR) of the reconstructed signal for a given total number of transform coefficients. First, the residual error, which is the difference between the original signal and the reconstructed signal, is properly formulated. Then, two gradient techniques, in conjunction with an optimization strategy, are developed to minimize the residual error. Sample results using this approach for representing synthetic signals and speech signals employing mixed Fourier/Walsh and Fourier/Haar transforms are given to illustrate the efficiency and accuracy of the proposed method