Hi , I have a problem with phase plot for Fourier series coefficients for periodic function exp(-t/2) , why phase plot is not odd function ?

% FS for exp(-t/2) periodic signal
% Compelx exponential FS
clc
clear;
a=0
b=pi
T0=b-a
N=11
F0=1/T0
wi=[-N:N]*2*pi/T0;
t=(a:0.2:b)';
D=zeros(2*N+1,1);
xt=exp(-0.5*t);
fun1 = @(t)exp(-0.5*t);
q1 = integral(fun1, a,b);
D(N+1)=q1/T0;
for n=1:N;
fun2 = @(t)exp(-0.5*t).*(exp(-j*2*pi*n*F0*t));
q2= integral(fun2,a,b,'ArrayValued',true);
D(N+1+n)=q2/T0;
fun3 = @(t)exp(-0.5*t).*(exp(j*2*pi*n*F0*t));
q3= integral(fun2,a,b,'ArrayValued',true);
D(N+1-n)=q3/T0;
end
% I Repeat the triangle pulse and plot for 7 periods
M=3; % The number of periods needed
tp=[];
xtp=[];
for i=-M:M
tp=[tp i*T0+t];
xtp=[xtp xt];
end

subplot(311)
plot(tp,xtp)
set(gca,'XMinorTick','on','YMinorTick','on')
ylabel('Peiodic decayed exponential function')
grid on
grid minor
subplot(312)
stem(-N:N,abs(D))
set(gca,'XMinorTick','on','YMinorTick','on')
ylabel('abs D_n')
grid on
grid minor
subplot(313)
stem(-N:N,angle(D))
set(gca,'XMinorTick','on','YMinorTick','on')
ylabel('Angle D_n')
grid on
grid minor

[Dimitris Kalogiros]

Use this button:

...in order to present your code under a "readable" format.

[Mohamad]

% FS for exp(-t/2) periodic signal % Compelx exponential FS clc clear; a=0 b=pi T0=b-a N=11 F0=1/T0 wi=[-N:N]*2*pi/T0; t=(a:0.2:b)'; D=zeros(2*N+1,1); xt=exp(-0.5*t); fun1 = @(t)exp(-0.5*t); q1 = integral(fun1, a,b); D(N+1)=q1/T0; for n=1:N; fun2 = @(t)exp(-0.5*t).*(exp(-j*2*pi*n*F0*t)); q2= integral(fun2,a,b,'ArrayValued',true); D(N+1+n)=q2/T0; fun3 = @(t)exp(-0.5*t).*(exp(j*2*pi*n*F0*t)); q3= integral(fun2,a,b,'ArrayValued',true); D(N+1-n)=q3/T0; end % I Repeat the triangle pulse and plot for 7 periods M=3; % The number of periods needed tp=[]; xtp=[]; for i=-M:M tp=[tp i*T0+t]; xtp=[xtp xt]; end

subplot(311) plot(tp,xtp) set(gca,'XMinorTick','on','YMinorTick','on') ylabel('Peiodic decayed exponential function') grid on grid minor subplot(312) stem(-N:N,abs(D)) set(gca,'XMinorTick','on','YMinorTick','on') ylabel('abs D_n') grid on grid minor subplot(313) stem(-N:N,angle(D)) set(gca,'XMinorTick','on','YMinorTick','on') ylabel('Angle D_n') grid on grid minor

Answer 1

[Torsten]

q3= integral(fun3,a,b,'ArrayValued',true);

instead of

q3= integral(fun2,a,b,'ArrayValued',true);

[Mohamad]

Thanks a lot , phase plot is odd now .