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# CTFS coefficients of a periodic square waveform

Language: Scilab

Processor: Not Relevant

Submitted by Senthilkumar R on Mar 21 2011

# CTFS coefficients of a periodic square waveform

This program is used to calculate the CTFS coefficients of a periodic square waveform
x(t) = 1, |t|<1, and 0, 1<|t|<2

//CTFS coefficients of a periodic square waveform
//x(t) = 1, |t|<T1, and 0, T1<|t|<T/2
clear;
close;
clc;
T =4;
T1 = T/4;
t = -T1:T1/100:T1;
Wo = 2*%pi/T;
xt =ones(1,length(t)); //Square Wave Generation
//Finding the Fourier Series Coefficients
for k =0:5
C(k+1,:) = exp(-sqrt(-1)*Wo*t.*k);
a(k+1) = xt*C(k+1,:)'/length(t);
if(abs(a(k+1))<=0.1)
a(k+1)=0;
end
end
a =a';
a_conj = real(a(:))-sqrt(-1)*imag(a(:));
ak = [a_conj(\$:-1:1)',a(2:\$)];
k = 0:5;
k = [-k(\$:-1:1),k(2:\$)];
Spectrum_ak = (1/2)*real(ak);
//Plotting the Continuous Time Signal
figure
a = gca();
a.y_location = "origin";
a.x_location = "origin";
a.data_bounds=[-2,0;2,2];
plot2d2(t,xt,5)
poly1 = a.children(1).children(1);
poly1.thickness = 3;
title('x(t)')
xlabel('                                                       t')
//Plotting the Spectral coefficients of CT Signal
figure
a = gca();
a.y_location = "origin";
a.x_location = "origin";
plot2d3('gnn',k,Spectrum_ak,5)
poly1 = a.children(1).children(1);
poly1.thickness = 3;
title('abs(ak)')
xlabel('                                                       k')
//Result
//Spectrum_ak  =
//0.0633127  0. -0.1055559 0. 0.3167197 0.5 0.3167197 0. -0.1055559    0.    0.0633127

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posted by Senthilkumar R