MATLAB: Daubechies filters: Frequency response

daubechiesfilterfrequency response

I need to know the frequency response of Db4 (6 levels) filters. I mean, I need to know the amplitude of the power spectral density (or similar) vs frequency (Hz)[using the frqz comand] for each of the levels of the Daubechies 4. Some one know how to do this?????

Best Answer

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');
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