An efficient representation of non-stationary signals using wavelets and mixed-transforms

A technique is presented to efficiently represent nonstationary signals by combining the wavelet and mixed-transforms. First, the signal is split into subbands using the discrete wavelet transforms. Next, each of these subbands is represented using superimposed partial sets of basis functions of different transforms, which are, in general, mutually nonorthogonal. 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 band for a fixed number of transform components. An optimization strategy is proposed to select the dominant components from the various domains for adaptation. These efficiently represented subbands are finally combined to reconstruct the signal.<>