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% This M-file demonstrate the signal components and Fourier Series
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% sigcomp.m --- plot the signal components and wave forms
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% Signal components:
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% Singal I: x(t)=3cos(20*pi*t-pi/4)+5cos(50*pi*t+pi/3)
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% fundamantal frequency is 10pi.
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T0=1/5;% 2pi/10pi
deltaT=T0/50; %50 samples per period
t=0:deltaT:2*T0;%plot 2 periods of the signal
x1=3*cos(20*pi*t-pi/4);% signal component 1
x2=5*cos(50*pi*t+pi/3);% signal component 2
x=x1+x2;% signal wave form
plot(t,x1,'b',t,x2,'r',t,x,'k');legend('x1','x2','x');
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pause
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% change the amplitude of the frequency components
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x1=4*cos(20*pi*t-pi/4);% signal component 1
x2=1.5*cos(50*pi*t+pi/3);% signal component 2
x=x1+x2;% signal wave form
figure;plot(t,x1,'b',t,x2,'r',t,x,'k');legend('x1','x2','x');
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pause
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% change the phase shift of the frequency components
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x1=3*cos(20*pi*t+pi/5);% signal component 1
x2=5*cos(50*pi*t-2*pi/5);% signal component 2
x=x1+x2;% signal wave form
figure;plot(t,x1,'b',t,x2,'r',t,x,'k');legend('x1','x2','x');
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pause
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% Another example
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w0=20*pi;
T0=1/10;
deltaT=T0/50;
t=0:deltaT:2*T0;
x0=1;
x1=sin(w0*t);
x3=1/3*sin(3*w0*t);
x5=1/5*sin(5*w0*t);
x7=1/7*sin(7*w0*t);
x9=1/9*sin(9*w0*t);
y1=x0+x1;
y3=y1+x3;
y5=y3+x5;
y9=y5+x7+x9;
figure;plot(t,y1,'b',t,y3,'r',t,y5,'g',t,y9,'k');
legend('dc+fund','upto3rd','upto5th','upto9th');
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pause
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% frequency components with phase shift
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x5=1/5*sin(5*w0*t+pi/4);
x7=1/7*sin(7*w0*t-pi/3);
x9=1/9*sin(9*w0*t+2*pi/3);
y5=y3+x5;
y9=y5+x7+x9;
figure;plot(t,y1,'b',t,y3,'r',t,y5,'g',t,y9,'k');
legend('dc+fund','upto3rd','upto5th','upto9th');
title('5th,7th,9th harmonics with phase shift');
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pause
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close all