Method estimating reflection coefficients of adaptive lattice filter and its application to system identification

In this paper, we propose a method of estimating the reflection coefficients of an adaptive lattice filter. In this method, conventional adaptive algorithms, for example, the normalized least mean square (NLMS) algorithm, are used for the estimation. In general, the reflection coefficients are estimated as cross-correlation coefficients between forward and backward prediction errors in each stage of the adaptive lattice filter. Accordingly, two divisions in each stage, and effectively doubling the number of stages, are required. A problem is that the processing cost of division is higher than that of multiplication, especially in cheap digital signal processors (DSPs). Hence, the reduction of the number of divisions is strongly desired in practical use. The proposed technique can decrease the number of divisions to one, provided that the NLMS algorithm is used. Moreover, in the application of the adaptive lattice filter, system identification is also important. In this paper, we present a technique for the application. The technique is derived from the proposed method.