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Whether convolution followed by down sampling equals wavelet decomposition

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Abhishek sadasivan
Abhishek sadasivan on 16 Aug 2016
Edited: Abhishek sadasivan on 16 Aug 2016
I know that wavelet decomposition equals convolution followed by down sampling by two.I tried to test this on mat lab on haar wavelet. I write the below code and compared with the default wavedec command in mat lab. The code I wrote is shown below.
% clear all
clc
h=[0.7071 0.7071];% Haar scaling filter
g=[-0.7071 0.7071];%Haar wavelet filter
x=[1:10];% Input
h=fliplr(h);% h(-m)
g=fliplr(g);%g(-m)
s=conv(h,x);
s=downsample(s,2)
d=conv(g,x);
d=downsample(d,2)
[a L]=wavedec(x,1,'haar') % for comparison
if true
% code
end
After running this program I get ` s = 0.7071 3.5355 6.3639 9.1923 12.0207 7.0710. d = 0.7071 0.7071 0.7071 0.7071 0.7071 -7.0710 and the wavedec out put as a = 2.1213 4.9497 7.7782 10.6066 13.4350 -0.7071 -0.7071 -0.7071 -0.7071 -0.7071. L = 5 5 10`
I dont know why wavedec and my code gives different out puts, will any one help???

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