An efficient representation of nonstationary signals using mixed-transforms with applications to speech

A useful 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 transform. Specifically, the subband splitting is performed by employing the scaling and the wavelet functions to low-pass and high-pass filter the signal. 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 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 and unvoiced speech signals are given to illustrate the accuracy of the proposed method. A specific class of scaling and wavelet functions are employed in conjunction with the mixed Fourier/Haar transforms. 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. Performance comparison is also presented for two different orders of scaling functions belonging to the same family