Hi,

I am trying to find the Fourier transform of this function

What I have got so far:

any thoughts would be very helpfull.

Thanks Alex.

Printable View

- Mar 22nd 2010, 08:24 AMjeneverboyfourier transform of f(x)=x, for 0<x<2
Hi,

I am trying to find the Fourier transform of this function

What I have got so far:

any thoughts would be very helpfull.

Thanks Alex. - Mar 22nd 2010, 11:41 PMCaptainBlack
- Mar 23rd 2010, 03:16 AMjeneverboy
allright, so

now Euler's formula can be used

here

plug in equation

now I use so equation becomes;

rewrite

so now there is a real part and a imaginary part:

is this correct so far?

does anyone have a suggestion how to simplify this?

thanks, Alex. - Mar 23rd 2010, 04:57 AMCaptainBlack
- Mar 23rd 2010, 06:10 AMjeneverboy
Hi,

I need an expression with sin and cos, because now I must evaluate

and

I can use the inverse transform here at a certain point which is a continuity point of .

inversion formula:

so this is because for instance at x=0 f is continuous, but for x=2 f is not continuous so there I can't use it.

But first I need an expression with cos and sin I think.

Alex. - Mar 23rd 2010, 06:30 AMCaptainBlack
- Mar 23rd 2010, 06:38 AMjeneverboy
ok here is the question I got

1a) Calculate the Fourier transform of the function

b)Evaluate

and

- Mar 23rd 2010, 06:49 AMCaptainBlack