How to plot gt please help me ????

syms y(x)

y(x) = piecewise(-0.5<x<0,(2+4*x),0<=x<+0.5,(2-4*x), 0);

figure; %tmin=-6;tmax=6;N=100; want these limits -6<=x<=6

fplot(y);

Answer 1

[Dimitris Kalogiros]

    clear; clc;

syms t g(x) x(t)

g(t) = piecewise(-0.5<t<0,(2+4*t),0<=t<+0.5,(2-4*t), 0)

x(t)=sym(0);
for k=-6:1:6
    x(t)=x(t)+g(t-k);
end

subplot(2,1,1); fplot(g, [-6 6 ]);
grid on; zoom on; ylim([-0.1 2.1])
xlabel('t'); ylabel('g(t)'); title('one period')

subplot(2,1,2); fplot(x, [-6 6 ]);
grid on; zoom on; ylim([-0.1 2.1])
xlabel('t'); ylabel('x(t)'); title('signal x(t)')

...and if you run it:

[yie don]

Can we able to find the complex fourier Series represtation of x(t)and mathamatical expression for xfs(t).

[Dimitris Kalogiros]

clear; clc;

%%definition of periodic signal
syms t g(x) x(t) 

g(t) = piecewise(-0.5<t<0,(2+4*t),0<=t<+0.5,(2-4*t), 0)

x(t)=sym(0);
for k=-6:1:6
    x(t)=x(t)+g(t-k);
end

subplot(2,1,1); fplot(g, [-6 6 ]);
grid on; zoom on; ylim([-0.1 2.1])
xlabel('t'); ylabel('g(t)'); title('one period')

subplot(2,1,2); fplot(x, [-6 6 ]);
grid on; zoom on; ylim([-0.1 2.1])
xlabel('t'); ylabel('x(t)'); title('signal x(t)')

%%fourier coefficients
syms a0  T k
syms a(k)

% in our example T=1 and -1/2<t<1/2

a_0=int(g(t),t,-1/2,1/2)

a(k)=int(g(t)*exp(-1i*k*(2*pi)*t),t,-1/2,1/2) 

% we are able to evaluate fourier coefficients for every k we like
a(1)
a(-1)
a(3)
a(-3)

[Adam]

Please don't use flags where a comment or voting for an answer is more appropriate. Flags are for reporting spam or inappropriate questions/answers/comments, not just for adding a comment about an answer.

Moved from flag:

"Flagged by yie don about 4 hours ago. Best anser"

[yie don]

sorry it was a mistake , and im a beginner

[yie don]

@Dimitris Kalogiros so i have to plot the fourier coefficinets for -101<= k<= +101 for the evaluation of the fourier series can we do it on the same graph with changing the above k limits for new limits or do we have to define a new k value for -t<= t <= 1 ??

[Dimitris Kalogiros]

This is my last contribution...

Keep in mind that for your example fourier coefficients are, after all, real numbers and are not zero for add index or 0.