Thread Subject: zero mirror images

Hello all,

I've often read about how, for a given set of zeros, an FIR filter can have the same amplitude response but different phase response by using the mirror images of its zeros. The mirror image in this case corresponds to the reciprocal of the conjugate of the original zero, or so I've read.

My problem is that I can't seem to be able to verify this with Matlab. I've been getting similar but not exact amplitude responses - and am unable to really understand why. My efforts I'll copy and paste below, would appreciate any input.

Thanks,
Alan

a = 0.7;
b = 0.2;

A = sqrt(a^2+b^2);
theta = atan(b/a);

r1 = A*exp(j*theta);
r2 = conj(r1);

b = conv([1 -r1],[1 -r2]);

% 1/z* = z/(A^2)
r3 = r1/(A^2);
r4 = conj(r3);

b_mir = conv([1 -r3],[1 -r4]);

H = freqz(b,1);
H_mir = freqz(b_mir,1);

figure;
hold on;
plot(20*log10(abs(H)));
plot(20*log10(abs(H_mir)),'r');