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MathGroup Archive 2004

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What is ListConvolve doing here?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46123] What is ListConvolve doing here?
  • From: "Ted Ersek" <ersekjm at tqci.net>
  • Date: Sat, 7 Feb 2004 04:02:04 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Consider the following:
   Off[General::spell1];
   Clear["Global`*"];
   listA={ a1, a2, a3, a4 };
   listB={ b1, b2, b3, b4, b5, b6 };

Next we have the basic use of ListConvolve:
   ListConvolve[ listA, listB ]

The next line gives the same result as the previous line.
   ListConvolve[ listA, listB, {-1,1}, listB, Times, Plus ]

Plus is Oderless and that makes it harder to see how ListConvolve makes 
the it's output.  In the next line I do the same as the previous lines 
except I use List where Plus was used earlier.
   ListConvolve[ listA, listB, {-1,1}, listB, Times, List ]

Below I have a few more examples using ListConvolve.
   ListConvolve[ listA, listB, {1,1}, listB, Times, List ]
   ListConvolve[ listA, listB, {2,-1}, listB, Times, List ]
   ListConvolve[ listA, listB, {-1,-2}, listB, Times, List ]

I can understand what LostConvolve does in the examples above.  In those 
examples I get a result very much like the convolution I learned about 
in school.  Can anyone help me understand what ListConvolve is doing in 
the examples below.  The output in these examples seems very different 
from the convolution I learned about in school.
   ListConvolve[ listB, listA, {1,-1}, listA, Times, List]
   ListConvolve[ listA, listB, {1,-1}, {s1,s2}, Times, List]

--------------------------
Thanks,
     Ted Ersek



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