Biquad Resonator

General JUCE discussion
1

I’m trying to do a simple resonator as a biquad filter. The thing works in principle, however when changing sample rate, the gain changes vastly.

The thing was derived as a direkt zero pole diagram with zeros on zero and poles at

radius * e^(+-i*omega)

with radius < 1.
The filter coefficients then read

m_b0 = 1
m_b1 = 0;
m_b2 = 0;

m_a1 = -2 * m_radius * cos(2 * M_PI * m_freq / m_samplerate);
m_a2 = m_radius * m_radius;

m_a0 is normalized as 1.

What am I doing wrong? If these coefficients are right then the biquad implementation is probably wrong, but I can’t find an error in neither.

2

not sure about your issue regarding the sample rate, but this page and its subsections explain the gain variations when varying the resonator’s freq (and how to compensate them) :
https://ccrma.stanford.edu/~jos/filters/Time_Varying_Two_Pole_Filters.html

1 Like
3

Hmmm while looking at your link, I realized that the two might be related. When changing the sample rate to double, I will only use the first half of the z-domain unit circle as the filter range. When the filter is not gain compensated (it is not) then I will get different gains.

But this begs the question: Will changing the samplerate change the frequency response of every digital filter ever? Since you basically have the same problem.

4

Ok I implemented the gain compensation and it helped a lot, the gain variance has gone from ripping my ears appart to slightly notable.

I think can fix the rest by introducing an empirically designed function which changes gain depending on the sample rate set.
Tanks! :slight_smile: