A Ramp Cosine Cepstrum Model for the Parameter Estimation of Autoregressive Systems at Low SNR

Shaikhanowarul Fattah,Wei-Ping Zhu,Momair Ahmad

doi:10.1155/2010/808312

Abstract

A new cosine cepstrum model-based scheme is presented for the parameter estimation of a minimum-phase autoregressive (AR) system under low levels of signal-to-noise ratio (SNR). A ramp cosine cepstrum (RCC) model for the one-sided autocorrelation function (OSACF) of an AR signal is first proposed by considering both white noise and periodic impulse-train excitations. Using the RCC model, a residue-based least-squares optimization technique that guarantees the stability of the system is then presented in order to estimate the AR parameters from noisy output observations. For the purpose of implementation, the discrete cosine transform, which can efficiently handle the phase unwrapping problem and offer computational advantages as compared to the discrete Fourier transform, is employed. From extensive experimentations on AR systems of different orders, it is shown that the proposed method is capable of estimating parameters accurately and consistently in comparison to some of the existing methods for the SNR levels as low as -5 dB. As a practical application of the proposed technique, simulation results are also provided for the identification of a human vocal tract system using noise-corrupted natural speech signals demonstrating a superior estimation performance in terms of the power spectral density of the synthesized speech signals.

Highlights

The parameter estimation of autoregressive (AR) systems under noisy conditions has been extensively studied in areas of signal processing, communication, and control
The ramp cosine cepstrum (RCC) model that we have developed based on the one-sided autocorrelation function (OSACF) ψx(τ) of noise-free signal can be used as a target function even when RCC is computed based on the OSACF of the noisy observation of the signal
We investigate the identification performance for synthetic AR signals as well as natural speech signals corrupted by additive noise

Summary

Introduction

The parameter estimation of autoregressive (AR) systems under noisy conditions has been extensively studied in areas of signal processing, communication, and control. Estimating the AR or linear predictive coding (LPC) parameters of a vocal tract (VT) system from an observed noisy speech plays an important role in speech coding, synthesis, and recognition [1]. Numerous system identification methods have been developed for both noisefree and noisy AR systems. The maximum likelihood (ML) methods are asymptotically consistent but their convergence performance relies heavily on the initialization process of the methods [2, 3]. The Yule-Walker (YW) methods have been widely employed to identify the AR systems [2]

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