# Resonant filter¶

**Author or source:**Paul Kellett**Created:**2002-01-17 02:07:02

```
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.
```

1 2 3 4 5 6 7 | ```
//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;
``` |

## Comments¶

**Date**: 2006-01-18 10:59:55**By**: mr.just starting

```
very nice! how could i turn that into a HPF?
```

**Date**: 2006-01-23 10:53:41**By**: ku.oc.mapson.snosrapsd@psd

```
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
```

**Date**: 2006-09-12 14:42:25**By**: uh.etle.fni@yfoocs

```
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
```