# How can I build Fourier series of a periodic rectangle pulse group with Matlab 6.5?

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#### turkerweb

##### Junior Member level 2 can anybody help me?

How can i build fourier series of a periodic rectangle puls group with Matlab 6.5?

for example like this...

what must be Matlab codes of this problem?

pls help.. #### echo47 fourier series coefficients matlab

ezplot('sin(x) + sin(3*x)/3');

ezplot('sin(x) + sin(3*x)/3 + sin(5*x)/5 + sin(7*x)/7 + sin(9*x)/9');

ezplot('sum(sin([1:2:33] .* x) ./ [1:2:33])');

#### palosian

##### Junior Member level 1 fourier matlab

i have te matlab codes and i can it to if you need it

#### turkerweb

##### Junior Member level 2 matlab code for fourier series

dear friends;

i have this codes but when i put this to Matlab ,i have take no result? i cant find where i do mistake (( can u help me?

%Rectanqual wave signs with fourier series
%
fig_size = [232 84 774 624];
T0 = 8;
w0 = 2*pi/8;
t = linspace(-8,16,1001);
a0 = 0.25;
n = 1:50;
an = (1./(pi*n)) .* sin(n*pi/2);
bn = (1./(pi*n)) .* (1 - cos(n*pi/2));
x1 = a0;
for i = 1:10
x1 = x1 + an(i)*cos(i*w0*t) + bn(i)*sin(i*w0*t);
end
x2 = x1;
for i = 11:30
x2 = x2 + an(i)*cos(i*w0*t) + bn(i)*sin(i*w0*t);
end
x3 = x2;
for i = 31:50
x3 = x3 + an(i)*cos(i*w0*t) + bn(i)*sin(i*w0*t);
end
A0 = a0;
An = sqrt(an.^2 + bn.^2);
thn = atan2(-bn,an)*180/pi;
X0 = A0;
Xn = An/2;
figure(1),clf,plot([-8 -6],[1 1],'b-',[-6 -6],[1 0],'b--',[-6 0],[0 0],'b-',[0 2],[1 1],'b-',[2 8],[0 0],'b-',...
[8 10],[1 1],'b-',[10 16],[0 0],'b-',[0 0],[0 1],'b--',[2 2],[1 0],'b--',[8 8],[0 1],'b--',...
[10 10],[1 0],'b--',[16 16],[0 1],'b--'),...
axis([-8 16 -.5 1.5]),plotax,xlabel('Time (s)'),ylabel('Amplitude'),title('Periodic Pulse Train x(t)'),...
set(gcf,'Position',fig_size),text(5,-0.2,'T_0 = 8 s'),text(5,-0.3,'Pulse width = T_0/4')
figure(2),clf,subplot(311),plot(t,x1),subplot(312),plot(t,x2),subplot(313),plot(t,x3),...
subplot(311),ylabel('Amplitude'),title('Fourier Series Representation of x(t) with 10 Terms'),...
subplot(312),ylabel('Amplitude'),title('Fourier Series Representation of x(t) with 30 Terms'),...
subplot(313),ylabel('Amplitude'),title('Fourier Series Representation of x(t) with 50 Terms'),xlabel('Time (s)'),...
for i = 1:3,subplot(3,1,i),...
hold on,plot([0 2],[1 1],'r-',[2 8],[0 0],'r-',[8 10],[1 1],'r-',[10 16],[0 0],'r-',...
[0 0],[0 1],'r--',[2 2],[1 0],'r--',[8 8],[0 1],'r--',[10 10],[1 0],'r--',[16 16],[0 1],'r--',...
[-8 -6],[1 1],'r-',[-6 -6],[1 0],'r--',[-6 0],[0 0],'r-'),hold off,...
axis([-8 16 -0.5 1.5]),plotax
end
set(gcf,'Position',fig_size)
figure(3),clf,subplot(211),plot(0,a0,'ro',n,an,'o'),axis([-5 50 -0.2 0.5]),plotax,...
hold on,plot([10.5 10.5],[-0.2 0.5],'r--',[30.5 30.5],[-0.2 0.5],'r--'),hold off,...
xlabel('Harmonic Number'),ylabel('Amplitude'),title('Trig Fourier Series Coefficients a_n for x(t)'),...
subplot(212),plot(n,bn,'o'),axis([-5 50 -0.05 0.35]),plotax,...
hold on,plot([10.5 10.5],[-0.05 0.35],'r--',[30.5 30.5],[-0.05 0.35],'r--'),hold off,...
xlabel('Harmonic Number'),ylabel('Amplitude'),title('Trig Fourier Series Coefficients b_n for x(t)'),...
set(gcf,'Position',fig_size)
figure(4),clf,subplot(211),plot(0,A0,'ro',n*w0,An,'o'),axis([-2*w0 16 -0.1 0.5]),plotax,...
xlabel('Frequency (r/s)'),ylabel('Magnitde'),title('Cosine Fourier Series Magnitudes A_n for x(t)'),...
subplot(212),plot(n*w0,thn,'o'),v=axis;axis([-2*w0 16 -200 10]),plotax,...
xlabel('Frequency (r/s)'),ylabel('Phase (deg)'),title('Cosine Fourier Series Phases Theta_n for x(t)'),...
set(gcf,'Position',fig_size)
figure(5),clf,subplot(211),plot(0,X0,'ro',n*w0,Xn,'o',-n*w0,Xn,'o'),axis([-16 16 -0.1 0.3]),plotax,...
xlabel('Frequency (r/s)'),ylabel('Magnitde'),title('Exponential Fourier Series Magnitudes X_n for x(t)'),...
subplot(212),plot(n*w0,thn,'o',-n*w0,-thn,'o'),v=axis;axis([-16 16 v(3:4)]),plotax,...
xlabel('Frequency (r/s)'),ylabel('Phase (deg)'),title('Exponential Fourier Series Phases Theta_n for x(t)'),...
set(gcf,'Position',fig_size)
clear i v
%
% ÖDEV BİTTİ *****

echo47 said:
ezplot('sin(x) + sin(3*x)/3');

ezplot('sin(x) + sin(3*x)/3 + sin(5*x)/5 + sin(7*x)/7 + sin(9*x)/9');

ezplot('sum(sin([1:2:33] .* x) ./ [1:2:33])');

u re super thnks and but i must show harmonic numbers of this series...i had written a code above but later i cant understand why i cant take result?can u check it pls...

#### echo47 fourier series in matlab

What is "plotax"? My MATLAB 7.0.1 complains, and I don't see it in the online help.
If I delete it, your code outputs several plots.

#### turkerweb

##### Junior Member level 2 plot exponential matlab

echo47 said:
What is "plotax"? My MATLAB 7.0.1 complains, and I don't see it in the online help.
If I delete it, your code outputs several plots.

no...that code came from a university teacher..my matlab 6.5 and so i cant use that codes,i couldnt understand problem..u say problem that at """plotax""",,,thnks but i dont know what it used for there,i hadnt no idea so i wanted help from you...

and now ,i suppose we found what is fault..and so whats the true code do i write ...withouth using plotax...

thnks , especially to echo47

#### echo47 fourier series matlab

When I delete the "plotax" words, your MATLAB code runs successfully, although it outputs some plots that I don't understand. Have you tried doing that?

#### turkerweb

##### Junior Member level 2 fourier matlab code

echo47 said:
When I delete the "plotax" words, your MATLAB code runs successfully, although it outputs some plots that I don't understand. Have you tried doing that?

Yes,i tried like that,its succesfull..u re right ,my friend..

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