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FIR Filter Structures 235
6.3.8 MATLAB IMPLEMENTATION
Given the impulse response h (n) orthe DFT H(k), we have to determine
the coefficients in (6.13) and (6.14). The following MATLAB function,
dir2fs, converts a direct form [h (n) values] to the frequency sampling
form by directly implementing (6.13) and (6.14).
function [C,B,A] = dir2fs(h)
% Direct form to Frequency Sampling form conversion
% -------------------------------------------------
% [C,B,A] = dir2fs(h)
% C = Row vector containing gains for parallel sections
% B = Matrix containing numerator coefficients arranged in rows
% A = Matrix containing denominator coefficients arranged in rows
% h = impulse response vector of an FIR filter
%
M = length(h); H = fft(h,M);
magH = abs(H); phaH = angle(H)’;
% check even or odd M
if (M == 2*floor(M/2))
L = M/2-1; % M is even
A1 = [1,-1,0;1,1,0]; C1 = [real(H(1)),real(H(L+2))];
else
L = (M-1)/2; % M is odd
A1 = [1,-1,0]; C1 = [real(H(1))];
end
k = [1:L]’;
% initialize B and A arrays
B = zeros(L,2); A = ones(L,3);
% compute denominator coefficients
A(1:L,2) = -2*cos(2*pi*k/M); A = [A;A1];
% compute numerator coefficients
B(1:L,1) = cos(phaH(2:L+1));
B(1:L,2) = -cos(phaH(2:L+1)-(2*pi*k/M));
% compute gain coefficients
C = [2*magH(2:L+1),C1]’;
In this function, the impulse response values are supplied through the
h array. After conversion, the C array contains the gain values for each
parallel section. The gain values for the 2nd-order parallel sections are
given first, followed by H (0) and H (M/2) (if M is even). The B matrix
contains the numerator coefficients, which are arranged in length-2 row
vectors for each 2nd-order section. The A matrix contains the denominator
coefficients, which are arranged in length-3 row vectors for the 2nd-order
sections corresponding to those in B, followed by the coefficients for the
1st-order sections.
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