A Tikhonov regularized RLS algorithm with an exponential weighting factor, i.e., a leaky RLS (LRLS) algorithm was proposed by the author. A quadratic version of the LRLS algorithm also exists in the literature of adaptive filters. In this letter, a cubic version of the LRLS filter which is computationally efficient is proposed when the length of the adaptive filter is short. The proposed LRLS filter includes only a divide per iteration although its multiplications and additions increase in number. Simulation results show that the proposed LRLS filter is faster for its short length than the existing quadratic version of the LRLS filter.

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.