I would like to write a 3 Band "EQ" with BiQuad Filters but for some reason, I get some phase distortion.
The problem already got discussed here.
I found out that I need to work with Allpass filters in order to compensate the phase response of my filters. Btw, the filters are Linkwitz-Riley 2nd order filters.
But when I try to copy the idea to my project, I still have some distortion.
// low pass calcuation for linkwitz riley filters
float lowCutoff; // the lower cutoff frequency
float highCutoff; // the higher cutoff frequency
double omega = M_PI * cutoffFrequency;
double theta = omega / sampleRate;
double kappa = omega / tan(theta);
double delta = kappa * kappa + omega * omega + 2.0 * kappa * omega;
double a0 = (omega * omega) / delta;
double a1 = 2.0 * a0;
double a2 = a0;
double b1 = (-2.0 * kappa * kappa + 2.0 * omega * omega) / delta;
double b2 = (-2.0 * kappa * omega + kappa * kappa + omega * omega) / delta;
// high pass, only the calculation of a0 to b2 changes
// the intermediate values stay the same
double a0 = (kappa * kappa) / delta;
double a1 = -2.0 * a0;
double a2 = a0;
double b1 = (-2.0 * kappa * kappa + 2.0 * omega * omega) / delta;
double b2 = (-2.0 * kappa * omega + kappa * kappa + omega * omega) / delta;
// allpass filter to compensate phase response:
double q = 0.5;
double alpha = (tan(M_PI*q/sampleRate) - 1) / (tan(M_PI*0.5/sampleRate) + 1);
double beta = -cos(lowCutoff * M_PI / sampleRate);
double a0 = -alpha;
double a1 = beta*(1.0 - alpha);
double a2 = 1.0;
double b1 = beta*(1.0 - alpha);;
double b2 = -alpha;;
Since I use 2nd order filters, I also have to use a 2nd order all pass filter, right?
I've read that for those filters and with this calculation, I hav to use q
. So q
should be the same as the q
in the Linkwitz-Riley filter, which should be 0.5
right? (I've read this somewhere, not sure about it.)
Then, my actual processing looks something like this:
// filter names:
// loAPF, lowHPF, ... low: lower cutoffhigh: higher cutoff
// APF: allpass, HPF: highpass, LPF: lowpass
highSample = lowAPF->tick(highHPF->tick(sample));
midSample = lowHPF->tick(highLPF->tick(sample));
lowSample = lowLPF->tick(highLPF->tick(sample));
Does somebody have any idea, why I might have problems with the phase response?
Thanks in advance!