       Re: moving average function

• To: mathgroup at smc.vnet.net
• Subject: [mg126323] Re: moving average function
• From: Matthias Odisio <matthias at wolfram.com>
• Date: Tue, 1 May 2012 05:22:06 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201204300840.EAA23629@smc.vnet.net>

```Bob,

On 4/30/12 3:40 AM, Robert McHugh wrote:
> Below is a moving average function that has the following features:
> 1. returns a list with the same length as the original length
> 2. provides a reasonable estimate for averages on the "sides" of the
> window.
>
> Have failed to figure out how to do this with ListConvolve and
> ListCorrelate, so I submit this with the hope that others can
> recommend how it might be improved. Also searched this website for
> alternatives but didn't find any that met the above criteria.
>
> I was motivated to do this in order to keep my code free of handling
> special cases related to the edges of the widow size.  Note that in
> one particular case, I have data measured every minute and would like
> to compare the results of using averaging the data over window sizes
> of 61, 121, and 181.
>
> Recommendations for how to improve the function or alternatives are
> appreciated.
> Bob.

MeanFilter truncates the sliding window at the boundaries:

In:= MeanFilter[listTest, 2]

Out= {1/3 (a + b + c), 1/4 (a + b + c + d),
1/5 (a + b + c + d + e), 1/5 (b + c + d + e + f),
1/5 (c + d + e + f + g), 1/5 (d + e + f + g + h),
1/5 (e + f + g + h + i), 1/5 (f + g + h + i + j),
1/5 (g + h + i + j + k), 1/4 (h + i + j + k), 1/3 (i + j + k)}

Matthias Odisio
Wolfram Research

> movingAverageBalanced[list_List, nAvg_Integer?OddQ ] :=
>  Module[{nHang, middle, left, right, all},
>   nHang = (nAvg - 1)/2;
>
>   middle = MovingAverage[list, nAvg];
>
>   left = Total[ Take[list, 2 # - 1]] /(2 # - 1) & /@ Range[nHang];
>   right =
>    Reverse[Total[ Take[list, -( 2 # - 1)]] /(2 # - 1) & /@
>      Range[nHang]];
>   all = Join[left, middle, right] ;
>   Return[all];
>   ]
>
> Example
> listTest = {a, b, c, d, e, f, g, h, i, j, k};
> r = movingAverageBalanced[listTest, 5];
> r // TableForm
>
> {
>  {a},
>  {1/3 (a + b + c)},
>  {1/5 (a + b + c + d + e)},
>  {1/5 (b + c + d + e + f)},
>  {1/5 (c + d + e + f + g)},
>  {1/5 (d + e + f + g + h)},
>  {1/5 (e + f + g + h + i)},
>  {1/5 (f + g + h + i + j)},
>  {1/5 (g + h + i + j + k)},
>  {1/3 (i + j + k)},
>  {k}
> }
>

```

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