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By using the wavelet toolbox it becomes possible to decompose and reconstruct a time series, e.g.

load leleccum; 
s = leleccum(1:3920); 

% decomposition
[c,l] = wavedec(s,3,'db5');

% Reconstruction
a0 = waverec(c,l,'db5');

From this, how is it possible to remove specific frequencies from the series? For example, once I have decomposed the series into its frequency components, how can I remove a frequency such as a daily cycle from it prior to reconstruction?

Example of signal with 24 unit cycle:

t = 1:365;
raw =  20+(10-2).*rand(1,length(t)); 
signal_1 = 10*sin(2*pi*t/24); 

y = raw + signal_1; % example data series

% decomposition
[c,l] = wavedec(y,3,'db5');

How would you remove the signal with a periodicity of 24 i.e. 'signal_1' from the final series?

Emma
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1 Answers1

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You'll need to modify the vectorsc and l that you get from wavedec. If you want to remove certain frequencies, find the data corresponding to those frequencies and zero it out. Then call call waverec to reconstruct the modified time series.

shoelzer
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  • thanks for your response. Although I understand the concept of removing certain frequencies and then reconstructing the array but when I use other packages for obtaining the wavelet coefficients it returns a matrix showing how each frequency varies in time. Therefore I am a bit confused as to why this command returns a vector i.e. not showing how similar frequencies varies in time, from 'c' I read this as showing all of the frequencies that make up the series, where none of the frequencies are repeated. Have I misunderstood its use? – Emma Feb 13 '13 at 14:45
  • Take a look at the [documentation for wavedec](http://www.mathworks.com/help/wavelet/ref/wavedec.html) to learn about the `c` and `l` vectors. – shoelzer Feb 13 '13 at 14:48
  • I have read through the documentation but am still unsure about the wavelet decomposition vector 'c', I have added an example code in my original post, would you be able to show me with this example how the frequencies noted should be removed prior to reconstruction. – Emma Feb 14 '13 at 08:24
  • @user1155751 You have to figure out which parts of `c` and `l` correspond to your signal of interest. I don't have access to the wavelet toolbox so I don't think I can help any further. – shoelzer Feb 14 '13 at 15:19