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IIR Filter Structures 223
Brow = r(i:1:i+1,:); Arow = p(i:1:i+1,:);
[Brow,Arow] = residuez(Brow,Arow,[]);
B(fix((i+1)/2),:) = real(Brow); A(fix((i+1)/2),:) = real(Arow);
end
end
The dir2cas function first computes the z-domain partial fraction expansion
using the residuez function. We need to arrange pole-and-residue
pairs into complex conjugate pole-and-residue pairs followed by real poleand-residue
pairs. To do this, the cplxpair function from MATLAB can
be used; this sorts a complex array into complex conjugate pairs. However,
two consecutive calls to this function, one each for pole and residue
arrays, will not guarantee that poles and residues will correspond to each
other. Therefore a new cplxcomp function is developed, which compares
two shuffled complex arrays and returns the index of one array, which can
be used to rearrange another array.
function I = cplxcomp(p1,p2)
% I = cplxcomp(p1,p2)
% Compares two complex pairs which contain the same scalar elements
% but (possibly) at differrent indices. This routine should be
% used after CPLXPAIR routine for rearranging pole vector and its
% corresponding residue vector.
% p2 = cplxpair(p1)
%
I=[];
for j=1:1:length(p2)
for i=1:1:length(p1)
if (abs(p1(i)-p2(j)) < 0.0001)
I=[I,i];
end
end
end
I=I’;
After collecting these pole-and-residue pairs, the dir2cas function computes
the numerator and denominator of the biquads by employing the
residuez function in the reverse fashion.
These parallel-form coefficients are then used in the function
parfiltr, which implements the parallel form. The parfiltr function
uses the filter function in a loop using the coefficients of each biquad
stored in the B and A matrices. The input is first filtered through the FIR
part C and stored in the first row of a w matrix. Then the outputs of all
biquad filters are computed for the same input and stored as subsequent
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