Sum of fourier series:

I just have a quick question. How do I enter the formula shown above? I can't seem to get n = 1, 3, 5, ... I tried different code along the line of this:

syms k x
x = 1/2 + symsum(k^2, k, [1:2:15])

But there is an error message.

Also, on a side note, what's the purpose of syms and the "x" variable shown in the matlab documentation example where I got this code?

Answer 1

[John BG]

Philip

the 1st part of Walter's answer has syntax error:

• it's most likely that t will have a higher amount of elements than vector n
• therefore sin(n.*pi.*t) will always find one or more terms (of n) with a numel(n) href = ""</a> numel(t) mismatch

returning error, from the attempted d.*t

.

Let me suggest the following:

L=100;  
t=[0:2/L:2];
  x=zeros(1,numel(t));
  for  n = 1:2:15 
      x=x+ sin(n*pi*t)/n; 
  end;
  x=x+.5/pi
  plot(t,x);grid on

.

Increase L to improve signal time resolution.

.

if you find these lines useful would you please mark my answer as Accepted Answer?

To any other reader, if you find this answer of any help please click on the thumbs-up vote link,

thanks in advance for time and attention

John BG

<mailto:[e-mail] [e-mail]>

[Real Name]

This is more correct for the specific question.

x=ones(1,numel(t))./2;
  for  n = 1:2:15 
      x = x + 2*sin(n*pi.*t)/(pi*n); 
  end;
figure;
plot(t,x);
grid on

[Walter Roberson]

"the 1st part of Walter's answer has syntax error:"

No it does not. There was no indication that t was required to handle vectors.

[Ale gutierrez]

I don't understand why you divide x by./2

Answer 2

[Walter Roberson]

Easiest is to use a definite sum:

n = 1:2:15;
x = 1/2 + sum( 2./(pi*n) .* sin(n.*pi.*t) );

But you could use

syms n t
x = 1/2 + symsum( 2./(pi*(2*n-1)) .* sin((2*n-1).*pi.*t), n, 1, 8 );

[Real Name]

It says: Error using .* Matrix dimensions must agree.

Error in Hw1Prob13 (line 4) x = 1/2 + sum( 2./(pi*n) .* sin(pi*n.*t));

[Walter Roberson]

For vector t, if you are using R2016b or later,

n = (1:2:15).';
x = 1/2 + sum( 2./(pi*n) .* sin(n.*pi.*t) );

For previous versions,

n = (1:2:15).';
x = 1/2 + sum( bsxfun(@times, 2./(pi*n), sin( bsxfun(@times, n.*pi, t) ) ) );