This letter presents a new design method for approximate inverse systems using all-pass networks. The efficacy of approximate inverse systems for input and parameter estimation of nonminimum phase systems is well recognized. in the previous methods, only time domain design of FIR (finite impulse response) type approximate inverse systems were considered. Here, we demonstrate that IIR (infinite impulse response) type approximate inverse systems outperform the previous methods. A nonlinear optimization technique is adopted for designing the proposed system in the frequency domain. Numerical examples are also presented to show the effectiveness of the proposed method.

This letter extends the overfitting lattice filter for ARMA parameter estimation with additive noise proposed by Sun and Yahagi. A new way of calculating the lattice parameters is proposed, making their computation truly recursive. This simplifies the method in Ref.(1), and makes it suitable to the parameter estimation of high-order systems.

This paper is devoted to a new design method for infinite impulse response approximate inverse system of a nonminimum phase system. The design is carried out such that the convolution of the nonminimum phase polynomial and its approximate inverse system can be represented by an approximately linear phase all-pass filter. A method for estimating the time delay and order of an approximate inverse system is also presented. Using infinite impulse response approximate inverse systems better accuracy is achieved with reduced computational complexity. Numerical examples are included to show the effectiveness of the proposed method.

This paper deals with the problem of autoregressive (AR) spectral estimation from a finite set of noisy observations without a priori knowledge of additive noise power. A joint technique is proposed based on the high-order and true-order AR model fitting to the observed noisy process. The first approach utilizes the uncompensated lattice filter algorithm to estimate the parameters of the over-fitted AR model and is one-pass. The latter uses the noise compensated low-order Yule-Walker (LOYW) equations to estimate the true-order AR model parameters and is iterative. The desired AR parameters, equivalently the roots, are extracted from the over-fitted model roots using a root matching technique that utilizes the results obtained from the second approach. This method is highly accurate and is particularly suitable for cases where the system of unknown equations are strongly nonlinear at low SNR and uniqueness of solution from the LOYW equations cannot be guaranteed. In addition, fuzzy logic is adopted for calculating the step size adaptively with the cost function to reduce the computational time of the iterative total search technique. Several numerical examples are presented to evaluate the performance of the proposed scheme in this paper.