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

Abstract

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.

Intraframe quantization of speech line spectrum pairs for code‐excited linear prediction based coders in packet networks

“…The best way to reduce the bit rate without affecting the quantization quality is the use of vector quantization (VQ) [27][28][29][30][31].…”

Nonlinear backward ADPCM speech coding using kernel methods and online sparsification

“…In practice the normalized version of this algorithm, that is, the normalized LMS algorithm, is used to alleviate the dependency of the LMS adaptive filter on the statistics of the input signal. This algorithm is usually utilized in the context of ADPCM speech coding where the weight update equation is 0 < μ ≪ 1 is the convergence parameter to control the memory span of the predictor filter and therefore the convergence speed of the algorithm and is an estimate of the input signal variance.…”

“…The exponentially weighted recursive least‐squares (EW‐RLS) algorithm finds the solution of a deterministic optimization problem by way of minimizing the exponentially weighted cost function expressed at instant i as 0 < < λ ⩽ 1 is the weighting factor, also called the forgetting factor, controlling the memory span of the prediction. Using the matrix inversion lemma, one can derive a recursive realization of the EW‐RLS algorithm in backward speech signal prediction .…”

“…In particular previous investigations into utilizing nonlinear Volterra filters for speech coding have revealed that although “nonlinear techniques based on Volterra series expansion have an inherent ability to describe some nonlinear characteristics existent in the speech signal, they are not so useful in applications that require reconstruction, e.g. speech coding, as a result of their inherent instability” .…”

“…Motivated by these facts and the properties of the kernel adaptive filtering algorithms, we examine, in the study reported here, a solution to the problems encountered in the conventional implementation of nonlinear speech coding . In fact, employing various kernel adaptive filtering algorithms in the framework of the ADPCM technique for speech coding is studied here for the first time and results are reported.…”