Group Delay Question

[Inventor]

Hi, I'm implementing a Karplus-Strong string synthesis model of a guitar. It sounds great, but the frequeny is off, it sounds kind of muted or low in frequency.

The way Karplus-Strong works is you send a noise burst into an adder, then send the adder output through a delay line and a low-pass filter, then back to the adder. The output of the model is the adder's output.

OK, so I've got all that working just fine and all kinds of neat application thingies like a sequencer and monome-like keyboard controller, etc., but once again it sounds low in frequency especially for the higher notes/strings.

Now, in the Wikipedia page on Karplus-Strong it says that I should set the delay line to the frequency period minus the group delay of the filter at the string frequency. Or in other words, the total feedback delay should be the period of the desired funamental frequency.

We are currently running the filter, which is a second order low pass, at a cutoff of three times the fundamental. So what I need is the group delay of that filter at 1/3 of the cutoff frequency. Anyone care to enlighten me on how to calculate that? Thanks.

[yusynth]

Try this : http://www.dsprelated.com/showarticle/69.php
A delay may be compared to an all-pass filter therefore the calculations can be applied to it as well.

[Inventor]

Thank you yusynth, I can probably write a ChucK program to do that FFT calculation, though I was looking for an easier answer. Lazy me!