An adaptive FIR filter based on the least mean p-power error (MPE) criterion is investigated. First, some useful properties of MPE function are studied. Three main results are as follows: 1) MPE function is a convex function of filter coefficients; so it has no local minima. 2) When input process and desired process are both Gaussian processes, then MPE function has the same optimum solution as the conventional Wiener solution for any p. 3) When input process and desired process are non-Gaussian processes, then MPE function may have better optimum solution than Wiener solution. Next, a least mean p-power (LMP) error adaptive algorithm is derived and some application examples are presented. Consequently, when the signal is corrupted by an impulsive noise, the adaptive algorithm with p=1 is preferred. Furthermore, when the signal is corrupted by noise or interference, the adaptive algorithm with proper choice of p may be preferred. >

Least mean p-power error criterion for adaptive FIR filter

The aim of this paper is to provide an overview of Sparse Linear Prediction, a set of speech processing tools created by introducing sparsity constraints into the linear prediction framework. These tools have shown to be effective in several issues related to modeling and coding of speech signals. For speech analysis, we provide predictors that are accurate in modeling the speech production process and overcome problems related to traditional linear prediction. In particular, the predictors obtained offer a more effective decoupling of the vocal tract transfer function and its underlying excitation, making it a very efficient method for the analysis of voiced speech. For speech coding, we provide predictors that shape the residual according to the characteristics of the sparse encoding techniques resulting in more straightforward coding strategies. Furthermore, encouraged by the promising application of compressed sensing in signal compression, we investigate its formulation and application to sparse linear predictive coding. The proposed estimators are all solutions to convex optimization problems, which can be solved efficiently and reliably using, e.g., interior-point methods. Extensive experimental results are provided to support the effectiveness of the proposed methods, showing the improvements over traditional linear prediction in both speech analysis and coding.

/pdf/sparse-linear-prediction-and-its-applications-to-speech-4ayq938k53.pdf

Sparse Linear Prediction and Its Applications to Speech Processing

A robust linear prediction (LP) algorithms is proposed that minimizes the sum of appropriately weighted residuals. The weight is a function of the prediction residual, and the cost function is selected to give more weight to the bulk of small residuals while deemphasizing the small portion of large residuals. In contrast, the conventional LP procedure weights all prediction residuals equally. The robust algorithm takes into account the non-Gaussian nature of the excitations for voiced speech and gives a more efficient (less variance) and less biased estimate for the prediction coefficients than conventional methods. The algorithm can be used in the front-end features extractor for a speech recognition system and as an analyzer for a speech coding system. Testing on synthetic vowel data demonstrates that the robust LP procedure is able to reduce the formant and bandwidth error rate by more than an order of magnitude compared to the conventional LP procedures and is relatively insensitive to the placement of the LPC (LP coding) analysis window and to the value of the pitch period, for a given section of speech signal. >

On robust linear prediction of speech

Simple iterative algorithms are presented for L/sub 1/ and L/sub infinity / minimization (regression) based on a variant of Karmarkar's linear programming algorithm. Although these algorithms are based on entirely different theoretical principles to the popular IRLS (iteratively reweighted least squares) algorithm, they have almost identical matrix operations. Also presented are the results of a Monte Carlo study comparing the numerical convergence properties of the Karmarkar algorithm for L/sub 1/ minimization to those of an IRLS and a simplex algorithm. The test problem involves L/sub 1/ estimation of AR (autoregressive) model parameters. The Karmarkar algorithm outperformed IRLS by achieving higher numerical accuracy in fewer iterations. Techniques for reducing the computational cost per iteration of the Karmarkar L/sub 1/ algorithm are discussed. >

L/sub 1/ and L/sub infinity / minimization via a variant of Karmarkar's algorithm

A multivariate statistical combination forecasting method for product quality evaluation

Most methods for linear prediction of speech are based on a least square error criterion (L 2 criterion). In this paper, it is shown that the robustness of a least absolute error criterion (L 1 criterion) is particularly well adapted to the analysis of voiced sounds. The well-known linear programming L 1 algorithms have two important drawbacks: the stability of the synthesis filter is not guaranteed, and the computation load is too heavy for real time analysis. All these problems are alleviated by the new L 1 algorithm proposed in this paper. Experiments show comparable efficiency with classical L 2 methods.

J.-P. Solvay

Papers

Linear prediction of speech with a least absolute error criterion