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Example 1

Generate a 50 Hz 100 V p-p sinusoidal signal (choose 1 kHz sampling frequency and

simulation time from 0.0 to 0.1 sec). Obtain its Continuous Wavelet Transform

(CWT) coefficients by choosing db4 mother wavelet. Plot the CWT coefficients in

3-D space. Observe the plot. Now change the mother wavelet form db4 to morl,harr, db1, db2 etc and obtain the 3-D plot.

Solution:

t=0:0.001:0.1;

y=100*sin(2*pi*50*t);

scale_no=50;c=cwt(y,1:scale_no,'db4');

surf(c) % Surface 3D plot

shading interpcolormap(hsv)

rotate3d on

az=-10;el=16;

view(az,el)

xlabel('Translation');

ylabel('Scale');zlabel('coefficient');

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Example 2

Generate a 50 Hz and 100 Hz 100 V p-p sinusoidal signal (choose 1 kHz sampling

frequency and simulation time from 0.0 to 0.1 sec). Add these two signal. Obtain its

Continuous Wavelet Transform (CWT) coefficients by choosing db4 mother

wavelet. Plot the CWT coefficients in 3-D space. Observe the plot. Now change the

mother wavelet form db4 to morl, harr, db1, db2 etc and obtain the 3-D plot.

Solution:

t=0:0.001:0.1;

y1=100*sin(2*pi*50*t);

t=0:0.001:0.1;

y2=100*sin(2*pi*100*t);

y=y1+y2;

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Example 3

Generate a 50 Hz and 100 Hz 100 V p-p sinusoidal signal (choose 1 kHz sampling

frequency and simulation time from 0.0 to 0.05 sec for first signal and 0.05 to 0.1 sec

for second signal). Join these two signals. Obtain its Continuous Wavelet Transform

(CWT) coefficients by choosing db4 mother wavelet. Plot the CWT coefficients in3-D space. Observe the plot. Now change the mother wavelet form db4 to morl,

harr, db1, db2 etc and obtain the 3-D plot.

Solution:

t1=0:0.001:0.05;

y1=100*sin(2*pi*50*t1);

t2=0.05:0.001:0.1;

y2=100*sin(2*pi*100*t2);

y=[y1 y2];

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scale_no=50;% Continuous wavelet transform

c=cwt(y,1:scale_no,'db4');

surf(c) % Surface 3D plotshading interp

colormap(hsv)

rotate3d on

az=-10;el=16;

view(az,el)

xlabel('Translation');ylabel('Scale');

zlabel('coefficient');

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Example 4

Generate a 50 Hz noisy sinusoid by adding 2 kHz sinusoid with the 50 Hz sinusoid.

Now calculate the Discrete Wavelet Transform (DWT) of the above signal (choose

db4 mother wavelet and decomposition level upto 9 th level). Recompose the DWT

coefficients in different level and obtain a subplot of those including the originalsignal. Now change the mother wavelet form db4 to morl, harr, db1, db2 etc and

obtain the different subplot.

Solution:

t=0:0.0001:0.1;

y1=100*sin(2*pi*50*t);

t=0:0.0001:0.1;

y2=100*sin(2*pi*2000*t);

y=y1+y2;

[c,l]= wavedec(y,9,'db1');

d9=wrcoef('d',c,l,'db4',9);

d5=wrcoef('d',c,l,'db4',5);

d3=wrcoef('d',c,l,'db4',3);d1=wrcoef('d',c,l,'db4',1);

a9=wrcoef('a',c,l,'db4',9);a5=wrcoef('a',c,l,'db4',5);a3=wrcoef('a',c,l,'db4',3);

a1=wrcoef('a',c,l,'db4',1);

subplot(6,1,1); plot(y);text(1010,5,'Original signal');

subplot(6,1,2);plot(d1);text(1010,5,'Detail Level1');

subplot(6,1,3);plot(a1);text(1010,5,'Approx Level1');subplot(6,1,4);plot(d3);text(1010,5,'Detail Level3');

subplot(6,1,5);plot(a3);text(1010,5,'Approx Level3');

subplot(6,1,6);plot(a5);text(1010,5,'Approx Level5');

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Example 5

Generate a partial discharge signal using the Matlab code shown below. Analyze the

partial discharge signal using DWT

Solution:

%Matlab code to generate PD signalt1=0:0.0001:0.01;

y1=100*sin(2*pi*50*t1);

t2=0.01:0.0001:0.012;

y2=100*sin(2*pi*50*t2)+100*sin(2*pi*1000*t2).*exp(-10*t2);

t3=0.012:0.0001:0.1;

y3=100*sin(2*pi*50*t3);

t=[t1 t2 t3];y=[y1 y2 y3];

%Matlab code for DWT analysis

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ls=length(y);

[c,l]= wavedec(y,9,'db2')

d3=wrcoef('d',c,l,'db2',3);d1=wrcoef('d',c,l,'db2',1);

a1=wrcoef('a',c,l,'db2',1);a3=wrcoef('a',c,l,'db2',3);

subplot(5,1,1); plot(y);text(1010,5,'Original signal')

subplot(5,1,2);plot(d1);text(1010,5,'Detail Level1');subplot(5,1,3);plot(a1);text(1010,5,'Approx Level3');

subplot(5,1,4);plot(d3);text(1010,5,'Detail Level3');

subplot(5,1,5);plot(a3);text(1010,5,'Approx Level3');

Example 6

Take a transformer impulse test signal. Analyze the signal using Wavelet Packet

Transform (WPT) upto level 3.

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Solution:

T = wpdec(s1,5,'db1');plot(T)

ca1=wprcoef(T,[1 0]);

cd1=wprcoef(T,[1 1]);caa2=wprcoef(T,[2 0]);

cda2=wprcoef(T,[2 1]);

cad2=wprcoef(T,[2 2]);cdd2=wprcoef(T,[2 3]);

subplot(4,2,1); plot(s1,'-r');

axis tightsubplot(4,2,3);plot(ca1,'-k');

axis tight

subplot(4,2,4);plot(cd1,'-b');

axis tightsubplot(4,2,5);plot(caa2,'-k');

axis tightsubplot(4,2,6);plot(cda2,'-k');

axis tight

subplot(4,2,7);plot(cad2,'-b');axis tight

subplot(4,2,8);plot(cdd2,'-b');

axis tight