Re: Moving average / smoothing data
- To: mathgroup at smc.vnet.net
- Subject: [mg64066] Re: Moving average / smoothing data
- From: dh <dh at metrohm.ch>
- Date: Tue, 31 Jan 2006 01:14:11 -0500 (EST)
- References: <drk45d$stj$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Lea,
in your signal, the information and the "noise" are clearly
distinguished by their frequency. Therefore, "Digital Filters" is the
tool of choice. Application of Digital that you may find in a text book
about signal processing.
Here is an simple example (note that the filters depend on the sampling
rate):
tt=1.5*Sin[x]+0.5*Sin[20*x];
dat = Table[tt, {x, 0, 20, .1}];
fil5={-0.0839161, 0.020979, 0.102564, 0.160839, 0.195804, 0.207459,
0.195804,0.160839, 0.102564, 0.020979, -0.0839161}
fil10={-0.0559006, -0.0248447,
0.00294214, 0.02746, 0.0487087, 0.0666885, 0.0813992, 0.0928408,
0.101013,0.105917, 0.107551, 0.105917, 0.101013, 0.0928408, 0.0813992,
0.0666885,0.0487087, 0.02746, 0.00294214, -0.0248447, -0.0559006}
fil15={-0.0410557, -0.026393, -0.0127414, -0.000101122, 0.011528, 0.0221458,
0.0317525, 0.0403479, 0.047932, 0.054505, 0.0600667, 0.0646173,
0.0681565,0.0706846, 0.0722014, 0.072707, 0.0722014, 0.0706846,
0.0681565, 0.0646173,0.0600667, 0.054505, 0.047932, 0.0403479,
0.0317525, 0.0221458, 0.011528,-0.000101122, -0.0127414, -0.026393,
-0.0410557}
ListPlot[ListConvolve[fil5, dat]]
ListPlot[ListConvolve[fil10, dat]]
ListPlot[ListConvolve[fil15, dat]]
Daniel
Lea Rebanks wrote:
> Hi All,
>
> Given the following function & subsequent plot.
>
> tt={1.5*Sin[x]+0.5*Sin[20*x],1.5*Sin[x]};
> pp=Plot[Evaluate[tt],{x,0,20}];
>
>
> I am trying to get the best smoothing / moving average function closest
> to the underlying 1.5*sin[x]
>
> Has anyone got any suggestions? Please show coding in reply so I can
> plot & see result.
>
> I have similar noise on exponential data, so hopefully
> the moving average you recommend will work on that too.
>
> Many thanks for your attention.
>
> Lea Rebanks...
>
> PS I am using version 5.1
>
>