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Re: Change multiplication operations into convolution operations

• To: mathgroup at smc.vnet.net
• Subject: [mg73609] Re: Change multiplication operations into convolution operations
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 23 Feb 2007 04:28:58 -0500 (EST)
• Organization: Uni Leipzig
• References: <erjp4f$pt3$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de

Hi,

expr = C1 F1[t] ** F2[t] + C2 F3[t] ** F4[t] ** F1[t]

try

(expr //. NonCommutativeMultiply[any___, a_[t_], b_[t_]] :>
           (var = Unique[t]; NonCommutativeMultiply[any, function[Integrate[
           a[# - var]*b[var], var]][t]])) /.
     NonCommutativeMultiply[a_] :> a /. function -> Function


Regards
   Jens

Zhao, Liang wrote:
> If I want to change the multiplication operations  into convolution
> operations in an arbitrary function such as
> C1 F1[t] F2[t] + C2 F3[t] F4[t] F1[t],
> where Fi(t) represents functions of t and Ci represents constant, into
> C1 F1[t] * F2[t] + C2 F3[t] * F4[t] * F1[t], where "*" indicate
> convolution.
> 
> any good elegant way to do it? High appreciations!
> 
> Liang
> 
> 
> 

• Follow-Ups:
  • Change multiplication operations into convolution operations (result & follow up question)
    • From: "Zhao, Liang" <ZhaoL@MedImmune.com>