Umal-qura university

Effect of Adding Fundamental, third, fifth, and seventh Harmonics

Example

clc clear all close all

t=0:0.0001:8; ff=0.5;

% WE ARE USING SINE FUNCTION BECAUSE FROM EXPONENTIAL FORM OF FOURIER

% SERIES FINALLY WE ARE LEFT WITH SINE TERMS
y = (4/pi)*sin(2*pi*ff*t);
% COMPLEX AMPLITUDE = (4/(j*pi*k))
for k = 3:2:7 fh=k*ff;
x = (4/(k*pi))*sin(2*pi*fh*t); y=y+x;
end
plot(t,y,'linewidth',1.5);
title('A square wave with harmonics 1st, 3rd, 5th, and 7th'); xlabel('Time');
ylabel('Amplitude');

2. 
   Effect of Adding 1st to 17th harmonics
   

Example

clc clear all

t=0:0.0001:8; ff=0.5;

% WE ARE USING SINE FUNCTION BECAUSE FROM EXPONENTIAL FORM OF FOURIER

% SERIES FINALLY WE ARE LEFT WITH SINE TERMS
y = (4/pi)*sin(2*pi*ff*t);
% COMPLEX AMPLITUDE = (4/(j*pi*k))
for k = 3:2:17 fh=k*ff;
x = (4/(k*pi))*sin(2*pi*fh*t); y=y+x;
end
plot(t,y,'linewidth',1.5);
title('A square wave with harmonics 1st‐ 17th'); xlabel('Time'); ylabel('Amplitude');

3. 
   Effect of Adding 1st to 27th harmonics
   

Example
clc clear all
95
Department of Computer Engineering Umm Al Qura University, Makkah
close all


t=0:0.0001:8; ff=0.5;

% WE ARE USING SINE FUNCTION BECAUSE FROM EXPONENTIAL FORM OF FOURIER

% SERIES FINALLY WE ARE LEFT WITH SINE TERMS
y = (4/pi)*sin(2*pi*ff*t);
% COMPLEX AMPLITUDE = (4/(j*pi*k))
for k = 3:2:55 fh=k*ff;
x = (4/(k*pi))*sin(2*pi*fh*t); y=y+x;
end
plot(t,y,'linewidth',1.5);
title('A square wave with harmonics 1st to 27th'); xlabel('Time');
ylabel('Amplitude');

96

2. Synthesis of Triangular wave

The Complex Amplitude is given by:

Xk = (‐8/*pi^2*k^2) for k is an odd integer

0 for k for k is an even integer For f = 1/T = 25Hz