Re: Re: The click~ object and band limited impulses...

>
> how do you bandlimit a spike? that is always an interesting question.
>

from a paper by eli brandt: "A bandlimited impulse is a sinc
function, time-scaled so as to have one zero-crossing
per sample period."
you might want to read it a second time - well, at least, i had to
read it several times to understand...

basically this means, a single bandlimited impulse is identical to a
unit impulse, as the sample points fall on the
zero-crossings of the sinc function (so you don't "see" it in the
sampled version).

it gets more complicated if you are interested in a series of closely
spaced impulses to generate harmonic sounds
(impulse train). as long as the fundamental period is an integer
multiple of the sampling rate, you are fine.
but with any other period, the impulses naturally will fall inbetween
sampling points, forcing us to interpolate -
otherwise heavy aliasing would occur. and that's where the underlying
sinc-function becomes visible (and audible).

>> You can be creative about how you limit/modify the
>> bandwidth using any of the array of available filters on the output
>> of [click~].

there certainly is a lot of fun and creative potential in this
combination.
if the goal is to produce a bandlimited impulse _train_, though, you
will not get there by generating
a unit impulse and using available filters in msp.

i believe there is more than one way to do it right - i had some
success using DSF (discrete summation formulae).
yet, i haven't seen an implementation only with native maxmsp objects.

vb