A novel pipelined neural IIR adaptive filter for speech prediction

Abstract

The paper presents a pipelined neural IIR filter (PNIIR) for nonlinear speech prediction. It inherits the usual pipelined two layers architecture: the nonlinear modular cascaded subsections and linear combiner subsection, and the nonlinear and linear weights of each module are updated using an real-time learning algorithms. The PNIIR filter units the good tracking performance of the neural IIR network and the low computation load of the pipelined architecture. The performance analysis and complexity analysis are illustrated in this paper. The experimental study for speech prediction is also carried out to testify the efficiency of the proposed nonlinear filter.

Introduction

The prediction is of great importance for the modeling and coding of speech signals [1]. Speech prediction has been widely used in practical applications [2], [3], [4]. Linear adaptive prediction frameworks are available to the prediction of speech signals, but they do not perform well for speech signals due to their inherent nonlinearity and nonstationary. Therefore, numerous researchers have paid attention to the nonlinear adaptive prediction technologies and have shown its superiorities than the conventional linear adaptive prediction technologies [5], [6] accounting for the nonlinear nature of the speech signals. So far the most widely used nonlinear filters being available to nonlinear speech prediction are mainly the following categories: neural networks (NNs) and polynomial filters (PFs).

NNs have the prime advantages of adaptive learning ability based on optimization and statistical theories [7]. Therefore, different types of adaptive nonlinear filters based on NNs proposed in different types of literature, such as radial basis function networks (RBF) [8], recurrent neural network (RNN) [9], functional link artificial NNs [10], etc., are a powerful and effective tool in nonlinear prediction mechanism. Due to the feedback mechanism, RNNs can accurately model the nonlinear dynamic system [11] with smaller structures than nonrecursive neural networks. This characteristic enables it to be successfully applied in nonlinear prediction of speech signal. But the RNNs suffer from heavy computational burden. To improve the above drawback of RNNs, a computationally efficient nonlinear predictor called pipelined recurrent neural network (PRNN) was presented in the literature [12]. In the past few years, some new systems based on neural networks [13], [14], [15] were investigated to further enhance the nonlinear prediction ability for speech signals.

The polynomial filter also plays an important role in nonlinear prediction. Volterra filter is one of the most widely used polynomial filters due to its good nonlinear processing ability and its simple implementation architecture. Moreover, the truncated Volterra filter has been successfully applied in nonlinear prediction of speech signals [16], while its output is still linear with respect to various higher order kernels or impulse responses. However, the number of the Volterra coefficients required to model nonlinear system grows with the delays (or memories) and orders, which results in a heavy computational burden. In order to avoid the aforementioned problem, researchers devoted into the further research of these methods: low-complexity adaptive algorithms [17], [18] and low-complexity filtering constructions [19], [20]. Especially, a nonlinear adaptive joint process filter based on pipelined feedforward second-order Volterra architecture (JPPSOV) [21] is proposed to overcome the computational loads of the Volterra adaptive filter. In recent years, some new methods (such as the volterra-wiener series [22], modified normalized least mean M-estimate [23], pipelined set-membership approach [24], bilinear model [25], etc.) are introduced into Volterra filters, and a hierarchical pipelined adaptive Volterra filter [26] based alternative update mechanism was designed by Pang and Zhang. This sort of Volterra filters are powerful in nonlinear speech prediction. Yet, at the same time, the computational complexity of these filters still deserves to be further studied for the nested pattern of pipelined structure.

In this paper, addressing the computational complexity of two types of typical adaptive filters based on pipelined structure (such as PRNN and JPPSOV), a novel nonlinear filter with pipelined construction based on neural infinite impulse response (IIR) filter (PNIIR) is presented to model the nonlinear prediction system for speech signals. The proposed filter achieves a relatively lower computational complexity through the modularity of the pipelined realizations. Furthermore, different from PRNN, JPPSOV and neural IIR filter, the nonlinear prediction capability of the PNIIR filter is enhanced by the output’s combination of the linear combiner section and nonlinear standard IIR section.

The remainder of this paper is organized as follows. In Section 2, it gives a review of the basic knowledge of the nonlinear neural IIR adaptive filter. Section 3 introduces the novel modular network for pipelined neural IIR filter and derives its adaptive algorithm. The stability performance and convergence condition are presented in Section 4. Analysis of the computational complexity is given in Section 5. Section 6 presents the experimental study for nonlinear speech prediction to demonstrate the effectiveness of the proposed nonlinear filter by comparing with PRNN and JPPSOV. Finally, the conclusion is drawn in Section 7.