  In this paper, we use a matrix adaptive filter as the synthesis stage of a
Uniform Filter Bank (UFB) to reconstruct the input signal. We first develop the
mathematical theory behind it by applying the model of optimal filtering at the
synthesis stage of the UFB and obtaining an expression for the matrix Wiener
filter. We have developed a theorem which we use to simplify the expression
further. In the absence of required information about the analysis stage, we
use adaptive filtering to arrive at the Wiener solution. We use the Least Mean
Square (LMS) algorithm to update the filter coefficients. Through experimental
results, we find that the adaptive filter is convergent for a stable Wiener
filter.
