Employing Volterra filters in the ADPCM technique for speech coding: a comprehensive investigation

Although linear filters are useful in a various applications in the context of speech processing, there are several evidences for existence of nonlinearity in speech signals. Our main aim is to launch a comprehensive investigation into the exploitation of nonlinear Volterra filters in the context of the ADPCM-based speech coding technique, using two methods of forward prediction, based on the LS criterion, and backward prediction, based on both LMS and RLS adaptation algorithms. In any case, after solving some innate problems, for example, ill-conditioning and instability, schemes for optimum exploitation of nonlinear prediction are developed and simulation results are provided, tested with several performance criteria. With forward prediction a scheme is developed to detect and flag those frames for which, after stabilizing, including the quadratic predictor is beneficial. Scalar and vector quantisation methods are used for quantising the residual signal and the filter parameters, respectively. The results show that using this scheme a negligible improvement (up to 0.62 dB in the SNR) can be achieved, in spite of the increase in bit rate and complexity. With backward prediction two frame-based schemes are developed in which for each frame, after examining a set of quadratic filters, the best filter in the sense of the best quality of the reconstructed speech is selected. The ultimate schemes result in an improvement of up to 1.5 dB in the overall SNR of the reconstructed speech at the cost of a slight increase in the bit-rate, a short delay and a demanding increase in the complexity. Copyright © 2010 John Wiley & Sons, Ltd.