all pairs l m which will eventually result in m 2 fir filters because the size of q k is m by m l m 0 1 m u2212 1 having designed all m 2 firs an m by m correction matrix filter c z may be formed with the l m th entry being c l m z the transfer function of the l m th filter with coefficients as follows c l m c l m 0 c l m 1 c l m n u2212 1 t 23 designing m 2 fir filters in which each l m th filter l m 0 1 m u2212 1 is designed by minimizing the weighted squared error wse between corresponding fir filter actual frequency response samples is as follows where the specified frequency response samples q l m k k 0 1 p m are given in the first nyquist zone by 22 for each pair l m l m 0 1 m u2212 1 a corresponding fir c l m n n 0 1 n u2212 1 may be found such that the wse is minimized with the wse given by the following where u03b2 k is the weighting factor for k th frequency bin and is identical for all firs e g all l m pairs the last restriction may be removed if desired and u03b2 k may be replaced by u03b2 l m k by introducing vector and matrix notations the minimization of 25 may be reformulated as a weighted least squares problem and any minimization methods e g normal equations differentiation and completion of squares may be used to find filter coefficients c l m n.