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Resonant filter

References : Posted by Paul Kellett

Notes :
This filter consists of two first order low-pass filters in
series, with some of the difference between the two filter
outputs fed back to give a resonant peak.

You can use more filter stages for a steeper cutoff but the
stability criteria get more complicated if the extra stages
are within the feedback loop.

Code :
//set feedback amount given f and q between 0 and 1
fb = q + q/(1.0 - f);

//for each sample...
buf0 = buf0 + f * (in - buf0 + fb * (buf0 - buf1));
buf1 = buf1 + f * (buf0 - buf1);
out = buf1;


Added on : 18/01/06 by mr[ DOT ]just starting
Comment :
very nice! how could i turn that into a HPF?

Added on : 23/01/06 by dsp[ AT ]dsparsons[ DOT ]nospam[ DOT ]co[ DOT ]uk
Comment :
The cheats way is to use HPF = sample - out;
If you do a plot, you'll find that it isn't as good as designing an HPF from scratch, but it's good enuff for most ears.
This would also mean that you have a quick method for splitting a signal and operating on the (in)discreet parts separately. :) DSP

Added on : 12/09/06 by scoofy[ AT ]inf[ DOT ]elte[ DOT ]hu
Comment :
This filter calculates bandpass and highpass outputs too during calculation, namely bandpass is buf0 - buf1 and highpass is in - buf0. So, we can rewrite the algorithm:

// f and fb calculation
f = 2.0*sin(pi*freq/samplerate);
/* you can approximate this with f = 2.0*pi*freq/samplerate with tuning error towards nyquist */
fb = q + q/(1.0 - f);

// loop
hp = in - buf0;
bp = buf0 - buf1;
buf0 = buf0 + f * (hp + fb * bp);
buf1 = buf1 + f * (buf0 - buf1);

out = buf1; // lowpass
out = bp; // bandpass
out = hp; // highpass

The slope of the highpass out is not constant, it varies between 6 and 12 dB/Octave with different f and q settings. I'd be interested if anyone derived a proper highpass output from this algorithm.

-- peter schoffhauzer

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