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Effect of Wavelet Support on Noisy Data

In this example you demonstrate an instance of discontinuities in noisy data being represented more sparsely using a Haar wavelet than when using a wavelet with larger support. This example requires Signal Processing Toolbox.

Create a noisy square wave with 512 samples. Plot the square wave.

n = 512;
t = 0:0.001:(n*0.001)-0.001;
yn = square(2*pi*10*t)+0.02*randn(size(t));
plot(yn)
grid on
title('Noisy Signal')

Obtain the maximal overlap discrete wavelet transform (MODWT) of the signal using the haar wavelet. The haar wavelet has a support of length equal to 1

modhaar = modwt(yn,'haar');

Obtain the multiresolution analysis from the haar MODWT matrix and plot the first-level details.

mrahaar = modwtmra(modhaar,'haar');
figure
hs = stem(mrahaar(1,:));
grid on
hs.Marker = 'none';
hs.ShowBaseLine = 'off';
title('First-Level MRA Details Using Haar Wavelet')

Obtain the MODWT of the signal by using the db4 wavelet. The db4 wavelet has a support of length equal to 7.

moddb4 = modwt(yn,'db4');

Obtain the multiresolution analysis from the db4 MODWT matrix and plot the first-level details. The discontinuities are represented less sparsely using the db4 wavelet than the haar wavelet.

mradb4 = modwtmra(modhaar,'db4');
figure
hs = stem(mradb4(1,:));
grid on
hs.Marker = 'none';
hs.ShowBaseLine = 'off';
title('First-Level MRA Details Using db4 Wavelet')

See Also

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