[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:
> 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
> 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
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
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)
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