       Re: Discrete convolution problem

• To: mathgroup at smc.vnet.net
• Subject: [mg43456] Re: Discrete convolution problem
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 17 Sep 2003 07:59:29 -0400 (EDT)
• Organization: Universitaet Leipzig
• References: <bk6i7a\$gno\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

what may ListConvolve[] do ?

ListConvolve[ker, list] forms the convolution of the kernel ker with
list. \
ListConvolve[ker, list, k] forms the cyclic convolution in which the kth
\
element of ker is aligned with each element in list. ListConvolve[ker,
list, \
{kL, kR}] forms the cyclic convolution whose first element contains
list[] \
ker[[kL]] and whose last element contains list[[-1]] ker[[kR]]. \
ListConvolve[ker, list, klist, p] forms the convolution in which list is
\
padded at each end with repetitions of the element p. ListConvolve[ker,
list, \
klist, {p1, p2, ... }] forms the convolution in which list is padded at
each \
end with cyclic repetitions of the pi. ListConvolve[ker, list, klist, \
padding, g, h] forms a generalized convolution in which g is used in
place of \
Times and h in place of Plus. ListConvolve[ker, list, klist, padding, g,
h, \
lev] forms a convolution using elements at level lev in ker and list

Regards
Jens

"J. Guillermo Sanchez" wrote:
>
> Dear group, I have this problem
>
> Given two functions f[t] and g[t] I wish to obtain their discrete
> convolution in points t: {t0, t1, t2,  t3, ..} given with this pattern
> {f[t0+t1] g[t1-T,t0,t1],
> f[t0+t1] g[t2-T,t0,t1]+f[t1+t2] g[t2-T,t1,t2],
> f[t0+t1] g[t3-T,t0,t1]+f[t1+t2] g[t3-T,t1,t2]+ f[t2+t3] g[t3-T,t2,t3]}
>
> Some thing like this:
>       discreteConvolution[list, f[t], g[t], t] = "(Function to be
> defined)"
>
> them
>
> Inp[]:=discreteConvolution[{t0, t1, t2, t3},f[t], g[t], t]
>
> Out[]:=
> {f[t0+t1] g[t1-T,t0,t1],
> f[t0+t1] g[t2-T,t0,t1]+f[t1+t2] g[t2-T,t1,t2],
> f[t0+t1] g[t3-T,t0,t1]+f[t1+t2] g[t3-T,t1,t2]+
>   f[t2+t3] g[t3-T,t2,t3]}
>
> Thanks a lot of
>
> Guillermo

```

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