wavelet matlab plotting error

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carlo mars
carlo mars on 10 Oct 2016
Commented: Walter Roberson on 15 Oct 2016
I have a simple signal x(t)=2*cos(2*pi*500*t); I use wavelet wavedec(x,9,'db4') ; when I plot "ap9 = [0- 9.76]Hz" I must found zero because my signal is 500 Hz ; but the first and last second dnot equal to zero; why?
clear all;clc;
t(1)=0; va(1)=0; vb(1)=0; vc(1)=0; x(1)=0;
for i=2:100000
t(i)=t(i-1)+1e-4; %fs=10000
x(i)=2*cos(2*pi*500*t(i));
end
%wavelet
fs=10000;
[c,l]=wavedec(x,9,'db4');
ap9=appcoef(c,l,'db4',9);
L=max(size(x));
sized=max(size(ap9));
Ts=1/10000;
timemax=Ts*L;
ta=linspace(0,timemax,sized);
figure(3)
plot(ta,abs(ap9))
  4 Comments
Walter Roberson
Walter Roberson on 13 Oct 2016
I do not have enough experience with wavelets to know what you are encountering this problem.

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Answers (1)

Rodney Tan
Rodney Tan on 12 Oct 2016
Edited: Rodney Tan on 12 Oct 2016
The spike appeared at the start and end is the wavelet boundary effect of any given signal. It is cause by zero padding that taken into account at the start and end of the signal where wavelet decomposition computation took place. This is because wavelet is effective to pick up any abrupt changes for a given signal. You need to mirror your signal by using padarray command, then perform your wavelet decomposition, this eliminate the boundary effect.
padarray example
signal = 1:10
mirrorpadsignal = padarray(signal,[0 3],'symmetric','both')
Please be inform your padding size may need to be long [0 10] or more depend on the type of mother wavelet you use.
Hope I answer your question.
  3 Comments
Walter Roberson
Walter Roberson on 15 Oct 2016
You could click on http://www.mathworks.com/matlabcentral/profile/contact/6664770-rodney-tan to send email to Rodney Tan to ask Rodney to return to the question.
I do not know nearly enough about wavelets to be able to answer the question. It would probably take me several days of studying, perhaps a couple of weeks of studying, to answer your question. That is not something I have the resources for.

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