A Direct Approach For Representing Non-Stationary Signals Using Mixed Transforms

Recently, a mixed transform technique was suggested for representing non-stationary signals efficiently by superimposing two subsets of transform components in the Fourier and Walsh domains. An iterative method was used to obtain the dominant components from the two domains, to reproduce the signal. This paper describes an exact formulation of the residual error after partially extracting the weighted transform components from each domain. In addition, a computationally efficient implementation is proposed that employs direct transformation from the Fourier to the Walsh domain. Also, a gradient algorithm is developed to minimize the error by adaptively adjusting the weights associated with the selected subsets of the transform components. Computer simulations are given to demonstrate the effectiveness of the technique