Re: Moving average type process

• To: mathgroup at smc.vnet.net
• Subject: [mg18295] Re: Moving average type process
• From: dreiss at earthlink.net (David Reiss)
• Date: Fri, 25 Jun 1999 15:05:35 -0400
• Organization: Scientific Arts
• References: <7kpbdq\$4at@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <7kpbdq\$4at at smc.vnet.net>, Virgil Stokes
<virgil.stokes at neuro.ki.se> wrote:

> I wish to perform the following "moving average" type process on
> a list to generate a new list:
>
> Inputs:
>   wtlist = {w1,w2,w3}     -- weight list
>   inlist = {a,b,c,d,e,f}  -- any other list (>= 3 elements)
>
> Output:
>   outlist = {w1*a+w2*b+w3*c, w1*b+w2*c+w3*d, w1*c+w2*d+w3*e, w1*d+w2*e+w3*f}
>
> Note, outlist will always contain 2 less (Length[wtlist]/2) elements
> than in the input list (inlist).
>
> If w1=w2=w3=x, then
> the following works fine:
>
> outlist = x*Drop[Plus@@NestList[RotateRight,inlist,2],2]
>
> This is a weighted (from wtlist) sum over another list of arbitrary
> length (inlist). I would like to get a "fast" function for doing this when
> the weights are not equal.
>
> -- Virgil

Here is an example that should give you what you want along the
lines of what you are trying above:

In[1]:=
Plus @@ ({w1, w1, w3}#) & /@ Partition[{a, b, c, d, e, f}, 3, 1]

Out[1]=
{a w1 + b w1 + c w3, b w1 + c w1 + d w3, c w1 + d w1 + e w3,
d w1 + e w1 + f w3}

In Mathematica Version 4 the ListConvolve function
is the fastest way to do this, I believe.

In[2]:=
ListConvolve[{w1, w1, w3}, {a, b, c, d, e, f}]
Out[2]=
{b w1 + c w1 + a w3, c w1 + d w1 + b w3, d w1 + e w1 + c w3,
e w1 + f w1 + d w3}

Cheers,

David

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