AR and ARMA system identification techniques under heavy noisy conditions and their applications to speech analysis

System identification under noisy environment has axiomatic importance in numerous fields, such as communication, control, and signal processing. The system identification is to estimate and validate the parameters of the system from its output observations, a task that becomes very difficult when the system output is heavily noise-corrupted. The major objective of this research is to develop novel system identification techniques for an accurate estimation of the parameters of minimum phase autoregressive (AR) and autoregressive moving average (ARMA) systems in practical situations where the system input is not accessible and only noise-corrupted observations are available. Unlike conventional system identification methods in which only the white noise excitation is considered, both the white noise and periodic impulse-train excitations are taken into account in the methodologies developed with an aim of directly using them in speech analysis. A new ARMA correlation model is developed, based on which a two-stage correlation-domain ARMA system identification method is proposed. In the first stage, the new model in conjunction with a residue based least-squares (RBLS) model-fitting optimization algorithm is used to estimate the AR parameters. In the second stage, the moving average (MA) parameters are estimated from the residual signal obtained by filtering the observed data using the estimated AR parameters. With a view to overcome the adverse affect of noise on the MA part, a noise-compensation scheme using an inverse autocorrelation function (IACF) of the residual signal is also proposed. Cepstrum analysis has been popular in speech and biomedical signal processing. In this thesis, several cepstral domain techniques are developed to identify AR and ARMA systems in noisy conditions. First, a ramp-cepstrum model for the one-sided autocorrelation function (ACF) of the AR and ARMA signals is proposed, which is then used for the estimation of the parameters of AR or ARMA systems using the RBLS algorithm. It is shown that for the estimation of the MA parameters of the ARMA systems, either a direct ramp-cepstrum model-fitting based approach or a noise-compensation based approach can be adopted. Considering that, in the case of real signals, discrete cosine transform is more attractive than the Fourier transform (FT) in terms of the computational complexity, a ramp cosine cepstrum model is also proposed for the identification of the AR and ARMA systems. In order to overcome the limitations of the conventional low-order Yule-Walker methods, a noise-compensated quadratic eigenvalue method utilizing the low-order lags of the ACF, is proposed for the estimation of the AR parameters of the ARMA system along with the noise variance. For the estimation of the MA parameters, the new noise-compensation method, in which, a spectral factorization of the resulting noise-compensated ACF of the residual signal is used, is employed. In order to study the effectiveness of the proposed identification techniques, extensive simulations are carried out by considering synthetic AR and ARMA systems of various orders under heavy noisy conditions. The results demonstrate the significant superiority of the proposed techniques over some of the existing methods even under very low levels of SNR. Simulation results on the identification of human vocal-tract systems using natural speech signals are also provided, showing a superior performance of the new techniques. As an illustration of application of the proposed AR and ARMA system identification techniques to speech analysis, noise robust schemes for the estimation of formant frequencies are developed. Synthetic and natural phonemes including some naturally spoken sentences in noisy environments are tested using the new formant estimation schemes. The experimental results demonstrate a performance superior to that of some of state-of-the-art methods at low levels of SNR.

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