MATLAB: Plotting the bandpass characteristics of a wavlet and its dilations

spectrum wavelet

Hi,

I simply want to plot the bandpass characteristic of a 'db2' Wavelet and some of its dilations. – First idea: Plot the spectrum – Second idea: Take the low- and high pass filter values as frequency characteristics

How would you do that?!

Thanks!

Best Answer

Hi, Since the 'db2' wavelet is associated with a multiresolution analysis, you can use the scaling (lowpass) and wavelet (highpass) filters to obtain the bandpass characteristics.

The key is to determine the equivalent filters for a given level. To do this make use of the multirate Noble identities.

For example, the equivalent scaling filters at levels 1, 2, and 3 are as follows: (I'm assuming you have the Singal Processing Toolbox by using freqz())

[LoD,HiD] = wfilters('db2');
[H1,W1] = freqz(LoD);
LoD2 = upsample(LoD,2);
LoD2 = conv(LoD2,LoD);
[H2,W2] = freqz(LoD2);
LoD3 = upsample(LoD,4);
LoD3 = conv(LoD3,LoD2);
[H3,W3] = freqz(LoD3);
plot(W1,abs(H1),'b');
hold on;
plot(W2,abs(H2),'k');
plot(W3,abs(H3),'r');
legend('Level1','Level2','Level3');
title('Daubechies Extremal Phase Equivalent Scaling Filters');

Wayne

Related Solutions

MATLAB: Daubechies filters: Frequency response

Hi Lorena, you have to determine the equivalent filter at each level of the wavelet tree. As a simple example, I'll show you how to compare the db4 scaling filter at level 1 and level 2.

Note to get the equivalent scaling filter at level 2 you have to lowpass filter at level 1 followed by downsampling by two and then lowpass filter for level 2.

[LoD,HiD] = wfilters('db4');
[H1,W1] = freqz(LoD);
% getting the equivalent impulse response for level 2

scal2 = conv(upsample(LoD,2),LoD)./sqrt(2);
[H2,W2] = freqz(scal2);
plot(W1,abs(H1),'k'); hold on;
plot(W2,abs(H2),'r'); 
legend('Level 1 Scaling Filter','Level 2 Scaling Filter');
xlabel('Radians/sample'); ylabel('Magnitude');

This is for 1st and 2nd level db4 wavelet (detail) filters.

[LoD,HiD] = wfilters('db4');
[H1,W1] = freqz(HiD);
% getting the equivalent impulse response for level 2
wav2 = conv(upsample(HiD,2),LoD)./sqrt(2);
[H2,W2] = freqz(wav2);
plot(W1,abs(H1),'k'); hold on;
plot(W2,abs(H2),'r'); 
axis tight;
legend('Level 1 Wavelet Filter','Level 2 Wavelet Filter', ...
    'Location','SouthEast');
xlabel('Radians/sample'); ylabel('Magnitude');

MATLAB: How to evaluate the performance of the bandpass filter

Use the freqz function with the second output:

[f,d] = bandpass(y, fpass, fs);
freqz(d)

That will produce the Bode plot of the filter, using the Filter Visualisation Tool.

Best Answer

Related Solutions

MATLAB: Daubechies filters: Frequency response

MATLAB: How to evaluate the performance of the bandpass filter

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