Question

MATLAB

code starts here ---------

clear

T0=2;
w0=2*pi/T0;
f0=1/T0;
Tmax=4;
Nmax=15;

%---

i=1;
for t=-Tmax: .01:Tmax
T(i)=t;
if t>=(T0/2)
while (t>T0/2)
t=t-T0;
end
elseif t<=-(T0/2)
while (t<=-T0/2)
t=t+T0;
end
end
if abs(t)<=(T0/4)
y(i)=1;
else
y(i)=0;
end
i=i+1;
end
plot(T,y),grid, xlabel('Time (sec)'); title('y(t) square wave'); shg
disp('Hit return..');
pause
%---
a0=1/2;
F(1)=0; %dc freq
C(1)=a0;
for n=1:Nmax
a(n)=(2/(n*pi))*sin((n*pi)/2);
b(n)=0;
C(n+1)=sqrt(a(n)^2+b(n)^2);
F(n+1)=n*f0;
end
stem(F,abs,(C)), grid, title(['Line Spectrum: Harmonics = ' num2str(Nmax)]);
xlabel('Freq(Hz)'), ylabel('Cn'), shg
disp('Hit return...');
pause
%---
yest=a0*ones(1,length(T));
for n=1:Nmax
yest=yest+a(n)*cos(2*n*pi*T/T0)+b(n)*sin(2*n*pi*T/T0);
plot(T,y,T,yest),grid,
title(['Nmax = ' num2str(n)]), shg, pause(1)
end
code ends here ------

Modify the program so for the triangle waveform (A-1, T0 2) Triangular Wave 8A Znat 5 COS が形 n=1

Answer 1

MATLAB code is given in bold letters.

clc;
close all;
clear all;
T0=2;
w0=2*pi/T0;
f0=1/T0;
Tmax=4;
Nmax=15;
i=1;
a0=0;
F(1)=0;
A = 1; T0 =2;
n = 1:2:15;
a= 8*A./(n*pi).^2;
b=0;
C=sqrt(a.^2+b^2);
F(n+1)=n*f0;
stem([0 n],[a0 abs(C)]), grid, title(['Line Spectrum: Harmonics = ' num2str(Nmax)]);
xlabel('k'), ylabel('Ck')
disp('Hit return...');
pause
%---
t = -4:0.01:4;

for k=1:length(t)
  
x(k) = a0+sum(C.*cos(2*pi*n*t(k)/T0));

end

figure;plot(t,x);xlabel('time');
ylabel('Amplitude');title('x(t)');grid on;
title('Fourier series approximation with N = 15');
ylim([-1.5 1.5]);