# [PD] smallest possible value of a delay-time

Frank Barknecht fbar at footils.org
Mon May 17 19:47:31 CEST 2004

```Hallo,
Roman Haefeli hat gesagt: // Roman Haefeli wrote:

> yeah, the problem is karplus-strong-synthesis. the sound is generated by
> feedbacks, so the length of  the delay determines the frequency. if the grid
> of possible delay-values is 1 sample, you get very large spaces between the
> resulting frequencies. (f = srate / delayinsamples). it's not only about
> smaller than 1 sample, but more precise than a sample. have a look at the
> beginning of this discussion.

Yes. One problem is the highest possible frequency you can create with
Karplus-Strong synthesis.

There you have:

frequency of tone = 1/delay length in seconds

If you create a 1-sample-delay, your delay length is exactly
1/samplerate and freq would become == samplerate, also according to

But as the sample theorem tells us, you cannot create a signal with a
frequency that is larger than SR/2, so to actually make use of a
Karplus-Strong delayline, you'd need to make the delay at least 2
samples long.

The other, more interesting problem is, can you and how could you get
around the quantization of possible pluck frequencies according to
above formula? Do you need to oversample to get delays with fractional
samples length? Like when you want to synthesize a pluck with a
frequency of 16000 Hz in CD quality, you'd need a delay length of
44100.0 / 16000.0 ~= 2.75 samples. Or is this possible with some kind
of interpolation like in a wavetable oscillator or does it require
oversampling? I think, it should be possible with interpolation, but
I'd have to dig out those DSP books for that or search the music-dsp
archive...

Ciao
--
Frank Barknecht                               _ ______footils.org__

```