State variable

Type : 12db resonant low, high or bandpass
References : Effect Deisgn Part 1, Jon Dattorro, J. Audio Eng. Soc., Vol 45, No. 9, 1997 September
Notes :
Digital approximation of Chamberlin two-pole low pass. Easy to calculate coefficients, easy to process algorithm.
Code :
cutoff = cutoff freq in Hz
fs = sampling frequency //(e.g. 44100Hz)
f = 2 sin (pi * cutoff / fs) //[approximately]
q = resonance/bandwidth [0 < q <= 1]  most res: q=1, less: q=0
low = lowpass output
high = highpass output
band = bandpass output
notch = notch output

scale = q

low=high=band=0;

//--beginloop
low = low + f * band;
high = scale * input - low - q*band;
band = f * high + band;
notch = high + low;
//--endloop

Comments
from : nope
comment : Wow, great. Sounds good, thanks.

from : no[DOT]spam[AT]plea[DOT]se
comment : The variable "high" doesn't have to be initialised, does it? It looks to me like the only variables that need to be kept around between iterations are "low" and "band".

from : nobody[AT]nowhere[DOT]com
comment : Right. High and notch are calculated from low and band every iteration.

from : neolit123[AT]gmail[DOT]com
comment : here is the filter with 2x oversampling + some x,y pad functionality to morph between states: like this fx (uses different filter) http://img299.imageshack.us/img299/4690/statevarible.png smoothing with interpolation is suggest for most parameters: //sr: samplerate; //cutoff: 20 - 20k; //qvalue: 0 - 100; //x, y: 0 - 1 q = sqrt(1 - atan(sqrt(qvalue)) * 2 / pi); scale = sqrt(q); f = slider1 / sr * 2; // * 2 here instead of 4 //----------sample loop //set 'input' here //os x2 for (i=0; i<2; i++) { low = low + f * band; high = scale * input - low - q * band; band = f * high + band; notch = high + low; ); // x,y pad scheme // // high -- notch // | | // | | // low ---- band // // // use two pairs //low, high pair1 = low * y + high * (1-y); //band, notch pair2 = band * y + notch * (1-y); //out out = pair2 * x + pair1 * (1-x); //----------sample loop

from : kb[AT]kebby[DOT]org
comment : One drawback of this is that the cutoff frequency can only go up to SR/4 instead of SR/2 - but you can easily compensate it by using 2x oversampling, eg. simply running this thing twice per sample (apply input interpolation or further output filtering ad lib, but from my experience simple linear interpolation of the input values (in and (in+lastin)/2) works well enough).

from : lala[AT]no[DOT]go
comment : Anyone know what the difference is between q and scale?

from : jabberdabber[AT]hotmail[DOT]com
comment : "most res: q=1, less: q=0" Someone correct me if I'm wrong, but isn't that backwards? q=0 is max res, q=1 is min res. q and scale are the same value. What the algorithm is doing is scaling the input the higher the resonance is turned up to prevent clipping. One reason why I think 0 equals max resonance and 1 equals no resonance. So as q approaches zero, the input is attenuated more and more. In other words, as you turn up the resonance, the input is turned down.

from : does[AT]not[DOT]matter
comment : scale = sqrt(q); and //value (0;100) - for example q = sqrt(1.0 - atan(sqrt(value)) * 2.0 / PI); f = frqHz / sampleRate*4.; uffffffff :) Now enjoy!