This paper relates to a novel algorithm for fast estimation of the coefficients of the adaptive FIR filter. The novel algorithm is derived from a first order IIR filter experssion clarifying the estimation process of the NLMS (normalized least mean square) algorithm. The expression shows that the estimation process is equivalent to a procedure extracting the cross-correlation coefficient between the input and the output of an unknown system to be estimated. The interpretation allows to move a subtraction of the echo replica beyond the IIR filter, and the movement gives a construction with the IIR filter coefficient of unity which forms the arithmetic mean. The construction in comparison with the conventional NLMS algorithm, improves the covergence rate extreamly. Moreover, when we use the construction with a simple technique which limits the term of calculating the correlation coefficient in the beginning of a convergence process, the convergence delay becomes negligible. This is a very desirable performance for acoustic echo canceller. In this paper, double-talk and echo path fluctuation are also studied as the first stage for application to acoustic echo canceller. The two subjects can be resolved by introducing two switches and delays into the evaluation process of the correlation coefficient.

It is sometimes required to change the frequency characteristics of a digital filter during its operation. In this paper a new synthesis of variable even-order IIR digital filters is proposed. The cut-off frequency of the filter can be changed by a single parameter. The fundamental filter structure is a cascade of second-order sections. The multiplier coefficients of each section are determined by using the Taylor series expansion of the lowpass to lowpass frequency transformation. For this method any second-order section can be used as a prototype, but here in this paper only the direct form and the lattice form are described. Unlike the conventional method, any transfer functions can be used for the proposed method. Finally a designed example shows that the proposed filter has wider tuning range than the conventional filter, and the advantage of the proposed filters is confirmed.