Wavelet decomposition (Meyer) for a signal

Hi everyone,

I want to decompose a signal with wavelet decomposition. The aim is to compare the IMF from EMD with wavelet decomposition.

Initially i used this function

[c,l] = wavedec(x,n,wname) returns the wavelet decomposition of the 1-D signal x at level n using the wavelet wname. The output decomposition structure consists of the wavelet decomposition vector c and the bookkeeping vector l, which contains the number of coefficients by level.

with:

A: raw data

n: 8

wname: meyer

When i try this i have this message:

[C,S] = wavedec(A,8,meyer);

Not enough input arguments.

Error in meyer (line 34)

tmp = log(N)/log(2);

What is the problem?

Is this the best way to obtain a multi-scale decomposition with Wavelet's method?

Thanks.

Answer 1

[Umeshraja]

Hi @Thomas PLOCOSTE,

To decompose a signal using the Meyer wavelet, you should use "dmey" as the wavelet name. Here's an example which include 8-level wavelet decomposition and plotting the coefficients:

load kobe.mat
A=kobe;
n=4;

% Perform wavelet decomposition
[C,S]=wavedec(A,n,"dmey");

%Extract and plot approximation Coefficients
approx = appcoef(C,S,"dmey");
subplot(n+1,1,1)
plot(approx)
title('Approximation Coefficients')

for i = 1:n
    % Extract detail coefficients for each level
    D = detcoef(C, S, i);
    % Plot the detail coefficients
    subplot(n+1, 1, i+1);
    plot(D);
    title(['Detail Coefficients at Level ', num2str(i)]);
end

Additionally, you can use the Wavelet Signal Analyzer app to decompose any 1-D signal. You can launch the app with the following command:

>>waveletSignalAnalyzer

For more information on using the app, please refer to the

https://www.mathworks.com/help/wavelet/ug/using-wavelet-signal-analyzer-app.html

To learn more about wavelet decomposition, you can consult the following resources

1-D Transform - https://www.mathworks.com/help/wavelet/ref/wavedec.html#d126e122098

2-D Transform - https://www.mathworks.com/help/wavelet/ref/wavedec2.html