# Regarding Wavelets and DWT.

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Sriram G on 25 Mar 2013
Edited: zaineb sadek on 2 Feb 2019
Hi everybody,
Since am a Dummie for image processing,I need to know about Multiresolution analysis with "WAVELETS" and
How does "Wavelet Transform" differs from fourier transform ?
And how to apply DWT to an image using MATLAB ?
what does the four subbands LL, LH, HL, HH meant for ?
Thanks a lot. Give your hand to my ignorance :-D

Carlos on 25 Mar 2013
Basically the wavelet transform is similar to the STFT(Short time Fourier Transform), because it links the frecuency of a signal to the time instant where that specific frecuency is happening.
However, the Wavelet transform has different resolutions depending on the frecuency.At high frecuency it has a high resolution, whereas at low frecuency it has low resolution. The STFT has a constant time resolution, that depends on the selected window length.
The DWT algorithm decomposes the image into 4 subband (subimage) ie,LL,LH,HL,HH. LL is the low frequency subband so it is used for further decomposition process.. LH subband extracts the horizontal features of original image. HL subband gives vertical features HH subband gives diagonal features.
However type doc cwt, for further details
Hope it helps
##### 1 CommentShowHide None
Sriram G on 28 Mar 2013
Hey Carlos !
I do understand :-D
Thanks a lot ! If some doubts come, I will ask :-D

### More Answers (1)

zaineb sadek on 2 Feb 2019
Edited: zaineb sadek on 2 Feb 2019
Hi Everyone, I faced a problem to apply Wavelet for extraction ECG fetal Signal I know there are three steps you have to do which are :
1- Transform the noisy ECG mother and fetal signal to wavelet domain for finding DWT coefficients of each level (sub band).
2- Apply thresholding to obtain the estimated wavelet coefficients for each level. but i d'ont have a thresholding functions for detect ECG fetal .
3- Reconstruct the ECG signal which have the estimated wavelet coefficients by inverse DWT.
please I am looking for your help.
code :
Fs = 4e3;
Time = 40;
NumSamp = Time * Fs;
%% Mom's Heartbeat
% In this example, we shall simulate the shapes of the electrocardiogram
% for both the mother and fetus. The following commands create an
% electrocardiogram signal that a mother's heart might produce assuming
% a 4000 Hz sampling rate. The heart rate for this signal is approximately
% 89 beats per minute, and the peak voltage of the signal is 3.5 millivolts.
x1 = 3.5*ecg(2700).'; % gen synth ECG signal
y1 = sgolayfilt(kron(ones(1,ceil(NumSamp/2700)+1),x1),0,21); % repeat for NumSamp length and smooth
n = 1:Time*Fs';
del = round(2700*rand(1)); % pick a random offset
mhb = y1(n + del)'; %construct the ecg signal from some offset
t = 1/Fs:1/Fs:Time';
subplot(3,2,1); plot(t,mhb);
axis([0 2 -4 4]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Maternal Heartbeat Signal');
%% Fetus Heartbeat
% The heart of a fetus beats noticeably faster than that of its mother,
% with rates ranging from 120 to 160 beats per minute. The amplitude of the
% fetal electrocardiogram is also much weaker than that of the maternal
% electrocardiogram. The following series of commands creates an electrocardiogram
% signal corresponding to a heart rate of 139 beats per minute and a peak voltage
% of 0.25 millivolts.
x2 = 0.25*ecg(1725);
y2 = sgolayfilt(kron(ones(1,ceil(NumSamp/1725)+1),x2),0,17);
del = round(1725*rand(1));
fhb = y2(n + del)';
subplot(3,2,2); plot(t,fhb,'m');
axis([0 2 -0.5 0.5]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Fetal Heartbeat Signal');
sig_mix=fhb+mhb;
%%DWT
sig1=sig_mix
OPsig=wden(sig1,'rigrsure','s','sln',6,'sym7');
[CA,CD] = wavedec(OPsig,6,'sym7');
A=CA;
P = thselect(CA,'rigrsure');
CA = wthresh(CA,'h',P);
AA=CA;
Csig = waverec(CA,CD,'sym7');
figure()
subplot(211)
plot(Csig,'r')
subplot(212)
plot(sig_mix,'b')