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Mon Jun 7 12:09:39 CEST 2010

with a pure delay of a whole number of samples, you can get the impulse
response by sampling a sinc function with the correct delay and sample rate.

It happens that sampling a sinc with a whole number of samples delay, you
get an IR with one sample of amplitude 1 at the sinc's centre peak, and the
rest of the sample points fall on zeros of the sinc function, so the IR has
an amplitude of 0 at all other points.  Thus you get the single unit impulse
function for the impulse response.

I recall that it is likewise possible to synthesise a fractional delay
filter by sampling a sinc function with the correct delay- which if
fractional, gives you an infinite impulse response of mostly non-zero
values, which of course is impossible to use as a real filter.  Then you can
go about creating variously optimised bandlimited methods of approximating
this response for example by using different windows to sample the sinc.

There are also other methods such as using polynomial interpolation or

There are some notes on the mathematics of this here and on other pages
linked from here:


> -----Original Message-----
> From: pd-list-admin at [mailto:pd-list-admin at]On Behalf Of
> Larry Troxler
> Sent: Saturday, 15 May 2004 1:33 AM
> To: Roman Haefeli
> Cc: post pd-msg
> Subject: Re: [PD] smallest possible value of a delay-time
> On Fri, 14 May 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.
> >
> It's certainly possible to get bandlimited fractional sample delays, using
> all pass filters. I don't remember if the minimum possible delay of the
> filter (if it can give a fractional delay less than one sample). But this
> is the technique used to tune physical waveguide models.
> Try searching the web for "fractional" "waveguide" "allpass" or the like.
> Larry Troxler
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