Informatica

The aim of the given paper is the development of an approach for parametric identification of Wiener systems with piecewise linear nonlinearities, i.e., when the linear part with unknown parameters is followed by a saturation-like function with unknown slopes. It is shown here that by a simple data reordering and by a following data partition the problem of identification of a nonlinear Wiener system could be reduced to a linear parametric estimation problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. A technique based on ordinary least squares (LS) is proposed here for the estimation of parameters of linear and nonlinear parts of the Wiener system, including the unknown threshold of piecewise nonlinearity, too. The results of numerical simulation and identification obtained by processing observations of input-output signals of a discrete-time Wiener system with a piecewise nonlinearity by computer are given.

The goal of the paper is to get a method of Lithuanian speech diphthong modelling. We use a formant-based synthesizer for this modelling. The second order quasipolynomial has been chosen as the formant model in time domain. A general diphthong model is a multi-input and single-output (MISO) system, that consists of two parts where the first part corresponds to the first vowel of the diphthong and the second one – to the other vowel. The system is excited by semi-periodic impulses with a smooth transition from one vowel to the other. We derived the parametric input-output equations in the case of quasipolynomial formants, defined a new notion of the convoluted basic signal matrix, derived parametric minimization functional formulas for the convoluted output data. The new formant parameter estimation algorithm for convoluted data, based on Levenberg–Marquardt approach, has been derived and its stepwise form presented. Lithuanian diphthong /ai/ was selected as an example. This diphthong was recorded with the following parameters: PCM 48 kHz, 16 bit, stereo. Two characteristic pitches of the vowels /a/ and /i/ have been chosen. Equidistant samples of these pitches have been used for estimating parameters of MISO formant models of the vowels. Transition from the vowel /a/ to the vowel /i/ was achieved by changing excitation impulse amplitudes by the arctangent law. The method was audio tested, and the Fourier transforms of the real data and output of the MISO model have been compared. It was impossible to distinguish between the real and simulated diphthongs. The magnitude and phase responses only have shown small differences.

This paper presents an iterative autoregressive system parameter estimation algorithm in the presence of white observation noise. The algorithm is based on the parameter estimation bias correction approach. We use high order Yule–Walker equations, sequentially estimate the noise variance, and exploit these estimated variances for the bias correction. The improved performance of the proposed algorithm in the presence of white noise is demonstrated via Monte Carlo experiments.

The aim of the given paper is the development of an approach for parametric identification of Hammerstein systems with piecewise linear nonlinearities, i.e., when the saturation-like function with unknown slopes is followed by a linear part with unknown parameters. It is shown here that by a simple input data rearrangement and by a following data partition the problem of identification of a nonlinear Hammerstein system could be reduced to the linear parametric estimation problem. Afterwards, estimates of the unknown parameters of linear regression models are calculated by processing respective particles of input-output data. A technique based on ordinary least squares is proposed here for the estimation of parameters of linear and nonlinear parts of the Hammerstein system, including the unknown threshold of the piecewise nonlinearity, too. The results of numerical simulation and identification obtained by processing observations of input-output signals of a discrete-time Hammerstein system with a piecewise nonlinearity with positive slopes by computer are given.

The aim of the given paper is the development of optimal and tuned models and ordinary well-known on-line procedures of unknown parameter estimation for inverse systems (IS) using current observations to be processed. Such models of IS are worked out in the case of correlated additive noise acting on the output of the initial direct system (DS). The results of numerical investigation by means of computer (Table 1) are given.