Efficient Representation Of Non-Stationary Signals Using Wavelets And Mixed-Transforms

A useful technique is presented to efficiently represent non-stationary signals by combining the wavelet and mixed-transforms. First, the signal is split into subbands using the discrete wavelet transform. Next, each of these subbands is represented using superimposed partial sets of basis functions of different transforms, which are in general, mutually non-orthogonal. This is termed the mixed-transforms representation. The residual error, which is the difference between the original subband and the reconstructed subband is properly formulated. Adaptive algorithms are developed to minimize this error and to maximize the Signal to Noise ratio (SNR) of the reconstructed subband for a fixed number of transform components. An optimization strategy is also proposed to select the dominant components from the various domains for adaptation. These efficiently represented subbands are finally combined to reconstruct the signal. Sample results for representing voiced speech signals are given to illustrate the accuracy of the proposed method. It is verified that for a given number of coefficients, the proposed technique yields a significantly higher SNR of the reconstructed signal than using mixed-transforms alone or the wavelet transform followed by a single transform