Re: wavelet

• To: mathgroup at smc.vnet.net
• Subject: [mg114730] Re: wavelet
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Tue, 14 Dec 2010 06:56:49 -0500 (EST)

```On 12/13/10 at 3:50 AM, dauphinester at gmail.com (clansa) wrote:

>The order StandardDeviation[Flatten[dwd[{___,1},"Values"]] compute
>the standard deviation of all the wavelets coefficients dwd

>But I want to calculate standard deviations of the wavelets
>coefficients for each level of the decomposition Do you know the
>solution?

Here are a couple of ways

In[1]:= data = RandomReal[1, {16}];

In[2]:= dwd = DiscreteWaveletTransform[data];

In[3]:= Normal[dwd] /.
HoldPattern[a_ -> b_] :>
If[Length[b] > 1, {a, StandardDeviation[b]}, {a, {}}]

Out[3]= {{{0}, 0.342116}, {{1}, 0.342662}, {{0, 0},
0.429588}, {{0, 1}, 0.297391}, {{0, 0, 0}, 0.428882}, {{0, 0, 1},
0.297418}, {{0, 0, 0, 0}, {}}, {{0, 0, 0, 1}, {}}}

In[4]:= StandardDeviation /@ Most[dwd[{___, 1}, "Values"]]

Out[4]= {0.342662,0.297391,0.297418}

```

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