       Discrete convolution problem

• To: mathgroup at smc.vnet.net
• Subject: [mg43393] Discrete convolution problem
• From: "J. Guillermo Sanchez" <guillerm at usal.es>
• Date: Tue, 16 Sep 2003 04:35:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```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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