Re: Discrete convolution problem

• To: mathgroup at smc.vnet.net
• Subject: [mg43461] Re: Discrete convolution problem
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Wed, 17 Sep 2003 07:59:40 -0400 (EDT)
• Organization: AOL http://www.aol.com
• References: <bk6i7a\$gno\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```discreteConvolution[tm_?VectorQ, f_, g_, T_] :=
Tr /@
Table[f[tm[[j]]+tm[[j+1]]]*
g[tm[[i+1]]-T,tm[[j]],tm[[j+1]]],
{i,1,Length[tm]-1},{j,i}];

discreteConvolution[{t0,t1,t2,t3}, f, g, T]

{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]}

In article <bk6i7a\$gno\$1 at smc.vnet.net>, "J. Guillermo Sanchez"
<guillerm at usal.es> wrote:

<< 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]}
>><BR><BR>

```

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