Analytical model for the first and second moments of an adaptive interpolated FIR filter using the constrained filtered-X LMS algorithm

The authors present an analytical model for the mean weight behaviour and weight covariance matrix of an adaptive interpolated FIR filter using the LMS algorithm to adapt the filter weights. The particular structure of this adaptive filter determines that special analytical considerations must be used. First, the introduction of an interpolating block cascaded with the adaptive sparse filter requires that the input signal correlations must be considered. It is well known that such correlations are disregarded by the independence theory, which is the basis for the analysis of the LMS algorithm adapting FIR structures. Secondly a constrained analysis is used to deal mathematically with the sparse nature of the adaptive section. Experimental results demonstrate the effectiveness of the proposed analytical models as compared with the results obtained by classical analysis.