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

IOhannes m zmoelnig zmoelnig at iem.at
Fri May 14 10:00:31 CEST 2004

```Roman Haefeli wrote:
> hi
>
> i had a discussion with a teacher today. the topic was the smallest
> delay-time possible. in his opinion one sample is the atom of signal and
> cannot be divided anymore. in my opinion it should be possible to get
> shorter delays than 1 samples with interpolation. my argument was: it should
> be possible to set the values of each sample so, that the resulting signal
> would be similar to a digitized analogue signal with a shorter than 1 sample
> delay.
>
> Does anybody know a good explanation for this problem?

1. the granularity of a digital delay is *always* 1 sample.

2. the length of 1 sample depends on the sample-rate

3. there are techniques that allow changing the sample-rate in digital
domain

4. to get a higher resolution you can apply such techinque: upsampling
this can be done with interpolation (of course this should be non-linear
but convolution with a sinc()))

5. the delay-resolution will still be 1 sample

6. while the delay-resolution in your original digital signal would be
1/44100 seconds (at 44.1kHz), in your upsampled signal you might get a
resolution of 1/88200 seconds (upsampling by a factor of 2)

7. when downsampling the signal again to the original fs, you will keep
the fractional delay (assuming that your sample-resolution is not
limited (for instance to 16 bit))

8. conclusion: both of you are right !
in digital domain you can only delay by 1 sample; the trick is, that you
can change the sample-rate (!) without any data-loss (assuming your
upsampling) and thus producing delays that are not integer multiples of
the original sample-length; but the delay is still bound to 1 sample
(but of another fs)

>
> i konw, this haven't got anything to do with pd. but i think you are the
> right people to ask. by the way: if it is possible, how would a realization
> in pd look like?

you can do upsampling in pd with the [block~] object (see
doc/3.audio-examples/J08.up.downsampling.pd)
however, the up-/downsampling algorithms are very bad; the best you get
is linear interpolation, so you might want to do some filtering before
and after the re-sampling.

and you can do sample-wise delay with [z~] (as others have mentioned)

mfg.asd.r
IOhannes

```