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[131]:= MeanFilter[listTest, 2] Out[131]= {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} > } >