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MathGroup Archive 1999

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Re: Discrete Convolution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19015] Re: Discrete Convolution
  • From: Bruno Daniel <bruno.daniel at hadiko.de>
  • Date: Tue, 3 Aug 1999 13:44:50 -0400
  • Organization: University of Karlsruhe
  • References: <7nrddv$i60@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Alister

Why not just the direct implementation? 


\!\(Conv[a_List, b_List] := 
    Module[\n\t\t{la = Length[a], lb = Length[b]}, \n\t\t
      Table[\[Sum]\+\(i = Max[1, k - la]\)\%\(Min[lb, k - 1]\)a
              \[LeftDoubleBracket]k - i\[RightDoubleBracket] 
            b\[LeftDoubleBracket]i\[RightDoubleBracket], {k, 2, la + lb}]]\)


or expressed in InputForm:

Conv[a_List, b_List] := 
   Module[{la = Length[a], lb = Length[b]}, 
    Table[Sum[a[[k - i]]*b[[i]], 
      {i, Max[1, k - la], Min[lb, k - 1]}], {k, 2, la + lb}]]


Example:
In[40]:=Conv[{a,b,c},{e,f}]
Out[40]= {a e, b e + a f, c e + b f, c f}


Yours sincerely
  Bruno


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