How to sum and plot a series of functions?

I have to plot the sum of this series, with N = 24, and N = 120. It's supposed to be a square wave, because of the gibbs phenomenon, but I just keep getting it wrong.

This is my code

:k = 1;

s = 1;

y = 120;

x = 27;

for k = 1:24;

a(k) =(2/pi)*((1-(-1)^k)/k)*sin(k*x);

end

for s = 1:120;

u(s) =(2/pi)*((1-(-1)^s)/s)*sin(s*x);

end

plot(a);

figure;

plot(u);

Thank you for your time!

Answer 1

[Torsten]

n = 24;
k = 1:n;
part1 = @(x) sin(k*x)
part2 = (2/pi*(1-(-1).^k)./k).';
x = linspace(0,2*pi,100);
Snx = arrayfun(@(x)part1(x)*part2,x);
plot(x,Snx)

[Klaus Damasceno]

It worked our perfectly! Would you care to explain about the arrayfun and the @? Also, would it work fine for n = 120?

Thanks Torsten!

[Torsten]

function main
  n1 = 24;
  x1 = linspace(0,2*pi,100);
  Snx1 = series(n1,x1);
  n2 = 120;
  x2 = linspace(0,2*pi,200);
  Snx2 = series(n2,x2);
  plot(x1,Snx1,x2,Snx2)
end

function Sn = series(n,x)
  part1 = @(x) sin((1:n)*x)
  part2 = (2/pi*(1-(-1).^(1:n))./(1:n)).';
  Sn = arrayfun(@(x)part1(x)*part2,x);
end

Answer 2

[madhan ravi]

Loop not necessary use cumsum() instead

y = 120;
x = linspace(1,27,24);
k = 1:24;
a(k) =cumsum((2/pi).*((1-(-1).^k)/k).*sin(k.*x));
plot(x,a(k));
s = 1:120;
x=linspace(1,27,120);
u(s) =cumsum((2/pi).*((1-(-1).^s)./s).*sin(s.*x));
figure;
plot(x,u(s));

[Klaus Damasceno]

Thanks man! But the graphics are still weird.

[Klaus Damasceno]

Am I doing something wrong?

[Torsten]

The function should be plotted within a certain x-range, not for a single x-value.

[madhan ravi]

thanks Torsten , edited the answer

[Klaus Damasceno]

I see. The value was given on the exercise, but should run a loop for 1:27 than?

[Klaus Damasceno]

I think the formula is right, but I might just be plotting it in the wrong way.

[madhan ravi]

yes probably try the edited answer

[Klaus Damasceno]

Yeah, it got a lot better. The first is almost a square wave, but the second one is still weird. Maybe I should change the range of x and y?

[Klaus Damasceno]

[Klaus Damasceno]

I changed the Y also, so that I could plot it too. (matrix dimensions weren't the same)

y = linspace(-3*pi,3*pi,120);
x = linspace(-3*pi,3*pi,24);
k = 1:24;
a(k) =cumsum((2/pi).*((1-(-1).^k)/k).*sin(k.*x));
s = 1:120;
u(s) =cumsum((2/pi).*((1-(-1).^s)./s).*sin(s.*y));
plot(a(k));
figure;
plot(u(s));

[madhan ravi]

 
x = linspace(-3*pi,3*pi,24);
k = 1:24;
a(k) =cumsum((2/pi).*((1-(-1).^k)/k).*sin(k.*x));
s = 1:120;
y = linspace(-3*pi,3*pi,120);
u(s) =cumsum((2/pi).*((1-(-1).^s)./s).*sin(s.*y));
plot(a(k));
figure;
plot(u(s));