A two-stage least square identification method is proposed for estimating ARMA (autoregressive moving average) coefficients from speech signals. A pulse-train like input sequence is often employed to account for the source effects in estimating vocal tract parameters of voiced speech. Due to glottal and radiation effects, the pulse train, however, does not represent the effective voice source. The authors have already proposed a simple but effective model of voice source for estimating AR (autoregressive) coefficients. This letter extends our approach to ARMA analysis to wider varieties of speech sounds including nasal vowels and consonants. Analysis results on both synthetic and natural nasal speech are presented to demonstrate the analysis ability of the method.

This paper proposes a new robust adaptive processing algorithm that is based on the extended least squares (ELS) method with running spectrum filtering (RSF). By utilizing the different characteristics of running spectra between speech signals and noise signals, RSF can retain speech characteristics while noise is effectively reduced. Then, by using ELS, autoregressive moving average (ARMA) parameters can be estimated accurately. In experiments on real speech contaminated by white Gaussian noise and factory noise, we found that the method we propose offered spectrum estimates that were robust against additive noise.

The recursive least-squares filter and fixed-point smoother are designed in linear discrete-time systems. The estimators require the information of the system matrix, the observation vector and the variances of the state and white Gaussian observation noise in the signal generating model. By appropriate choices of the observation vector and the state variables, the state-space model corresponding to the ARMA (autoregressive moving average) model of order (n,m) is introduced. Here,some elements of the system matrix consist of the AR parameters. This paper proposes modified iterative technique to the existing one regarding the estimation of the variance of observation noise based on the estimation methods of ARMA parameters in Refs. [2],[3]. As a result, the system matrix, the ARMA parameters and the variances of the state and observation noise are estimated from the observed value and its sampled autocovariance data of finite number. The input noise variance of the ARMA model is estimated by use of the autocovariance data and the estimates of the AR parameters and one MA parameter.

In the actual acoustic environment, the stochastic process exhibits various non-Gaussian distribution forms, and there exist potentially various nonlinear correlations in addition to the linear correlation between time series. In this study, a nonlinear ARMA model is proposed, based on the Bayes' theorem, where no artificially pre-established regression function model is assumed between time series, while reflecting hierarchically all of those various correlation informations. The proposed method is applied to the actual data of road traffic noise and its practical usefulness is verified.

An adaptive method analyzing analytic speech signals is proposed in this paper. The method decreases the errors of finite precision on calculation in a method with real coefficients. It is shown from the results of experiments that the proposed method is more useful than adaptive methods with real coefficients.

This paper introduces some modelling methods of time-varying stochastic process and its linear/nonlinear adaptive identification. Time-varying models are often identified by using a least square criterion. However the criterion should assume a time invariant stochastic model and infinite observed data. In order to adjust these serious different assumptions, some windowing techniques are introduced. Although the windows are usually applied to a batch processing of parameter estimates, all adaptive methods should also consider them at difference point of view. In this paper, two typical windowing techniques are explained into adaptive processing. In addition to the use of windows, time-varying stochastic ARMA models are built with these criterions and windows. By using these criterions and models, this paper explains nonlinear parameter estimation and the property of estimation convergence. On these discussions, some approaches are introduced, i.e., sophisticated stochastic modelling and multi-rate processing.

This letter extends the Yule-Walker method to the estimation of ARMA parameters from output measurements corrupted by noise. In the proposed method it is assumed that the noise variance and the input are unknown. An algorithm for the estimation of noise variance is, therefore, given. The use of the variance estimation method proposed here together with the Yule-Walker equations allow the estimation of the parameters of a minimum phase ARMA model based only on noisy measurements of its output. Moreover, using this method it is not necessary to slove a set of nonlinear equations for MA parameter estimation as required in the conventional correlation based methods.