Thread: Fourier transform - odd funktion

I'm transforming f(x) = 1-x trying to do so in an even and odd fashion... I think I get it right for the even, but I get stuck while tinkering with the odd one.

The period is 2, odd distribution.

; &

= [integrate by parts] =

Here I get stuck because .

If anyone could point out what I'm overseeing..?

Originally Posted by liquidFuzz

I'm transforming f(x) = 1-x trying to do so in an even and odd fashion... I think I get it right for the even, but I get stuck while tinkering with the odd one.

The period is 2, odd distribution.

; &

= [integrate by parts] =

Here I get stuck because .

If anyone could point out what I'm overseeing..?

Do you integration by parts again more carefully.

CB

No, I can't nail it...

What if I change the interval over wish integrate to [-1,0] + [0,1]. Maybe that would make it easier, but will my series convert to the odd distribution of 1-t?

Edit: Oh crap, I just realised something. I think my series could be right. My conclusion on the contrary... I was so preoccupied with the fact that that I sorta forgot the variable t.

Does this compute..?

Originally Posted by liquidFuzz

No, I can't nail it...

What if I change the interval over wish integrate to [-1,0] + [0,1]. Maybe that would make it easier, but will my series convert to the odd distribution of 1-t?

Edit: Oh crap, I just realised something. I think my series could be right. My conclusion on the contrary... I was so preoccupied with the fact that that I sorta forgot the variable t.

Does this compute..?

If I recall correctly yes

CB

Originally Posted by CaptainBlack

If I recall correctly yes

CB

I plotted the series in MatLab and got a result that points in an other direction. :-(
Here's the plot I got and the MatLab code I wrote.
MatLab

Code:

N = 20;
x = (-50:50)/20;   %interval : [-2.5,2.5]
f = ones(1,101);
%Odd fourier, no a_0 and a_i included.
for i = 1:1:N       %from 1 to N 
    f = f + (2 * sin(pi*i*x))  /  (i * pi);  %sum all terms over N iterations.
end
plot(x,f)

The function I was aiming for is 1-t and it should hold the points [0,1] and [2,-1] and then jump to next 'slope'. Eh, right?

I guess my question is, is it the series or is the MatLab tinkering that's wrong..?

Originally Posted by liquidFuzz

I plotted the series in MatLab and got a result that points in an other direction. :-(
Here's the plot I got and the MatLab code I wrote.
MatLab

Code:

N = 20;
x = (-50:50)/20;   %interval : [-2.5,2.5]
f = ones(1,101);
%Odd fourier, no a_0 and a_i included.
for i = 1:1:N       %from 1 to N 
    f = f + (2 * sin(pi*i*x))  /  (i * pi);  %sum all terms over N iterations.
end
plot(x,f)

The function I was aiming for is 1-t and it should hold the points [0,1] and [2,-1] and then jump to next 'slope'. Eh, right?

I guess my question is, is it the series or is the MatLab tinkering that's wrong..?

Why did you initialise f to one?

Try:

f = zeros(1,101)

CB

Eh, good question..?

Thanks for your help and patience dude!