I need help with fourier matrix index integral, I can't find how to write it in matlab

I don't know how to type this into matlab. Fourier function with matrix index

Here is my mathcad code and I'm trying to learn how to write it in matlab:

The first part of my matlab code is i which corresponds with i(t) from mathcad photo. I can't find how to write the integral with matrice index.

%%

%current i(t)

T=20*10^-3;

t=0:T/1000:T;

w=2*pi*1/T;

i=100.*(t>1*T/12).*(t<5*T/12)-100.*(t>7*T/12).*(t<11*T/12);

u=sin(w*t).*10.*(t>0).*(t<T);

%plot i

figure(1)

plot(t,i, 'DisplayName', 'i(t)')

hold on

legend

xlabel('Time','FontSize',16)

title('3.20','FontSize',16)

%until here the code is working

%a0, an, ab

n = linspace(0, 50);

T=20*10^-3;

t=0:T/1000:T;

w=2*pi*1/T;

a0 = @(i,T) integral(@(t) 2./T.*i, 0, T);

an = @(i,T) integral(@(t) 2./T.*i.*cos(n*w*t), 0, T);

ab = @(i,T) integral(@(t) 2./T.*i.*sin(n*w*t), 0, T);

F=sum(an.*cos(n*w*t).+bn.*sin(n*w*t)

fourier=(a0/2)+F

%plot fourier + current

figure(2)

plot(t,i+fourier, 'DisplayName', 'fourier')

hold on

legend

xlabel('Time','FontSize',16)

title('3.20','FontSize',16)

It should plot like this:

Any help is appreciated thanks.

[Torsten]

You might want to learn MATLAB's basics here:

https://de.mathworks.com/learn/tutorials/matlab-onramp.html

Answer 1

[Torsten]

n = 50;
T=20*10^-3;
t=0:T/1000:T;
w=2*pi*1/T;
f=@(t)0+100.*(t>1*T/12).*(t<5*T/12)-100.*(t>7*T/12).*(t<11*T/12);
a0 = 2/T*integral(@(t)f(t),0,T);  
for i=1:n
    a(i) = 2/T*integral(@(t)f(t).*cos(w*i*t),0,T);
    b(i) = 2/T*integral(@(t)f(t).*sin(w*i*t),0,T);  
end
four = @(t) a0/2+sum((a(1:n).*cos((1:n)*w*t)+b(1:n).*sin((1:n)*w*t)));
four_eval = arrayfun(four,t)
plot(t,f(t))
hold on
plot(t,four_eval)

[Mircea Prisada]

Thank you very much! Also thank you for the link provided!