Fourier Transform

Discussion in 'Homework Help' started by smarch, May 9, 2010.

1. smarch Thread Starter Active Member

Mar 14, 2009
52
0
Hi

I am trying to find an expression for X(f), when,

x(t)=exp(-σt)sin(2∏f1t)

I have attached a screen shot of what I have worked out, but it doesn't seem to be coming together very vell, is there something I am missing in the steps? Or am I right, and how would I integrate that?

thanks.

File size:
15.8 KB
Views:
20
2. t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
The Fourier transform of

$u(t)\epsilon^{-\sigma t}sin(\omega_{1}t)$

per table of transforms is

$\frac{\omega_{1}}{\omega_{1}^2+(\sigma+j\omega)^2}$

The u(t) bit tells you the limits of integration are from 0 to plus infinity - otherwise there is no solution if the lower limit goes to minus infinity . The problem can be solved using repeated integration by parts.

Not sure if this is the same as your problem - given your equation has no reference to the u(t) term - i.e. the Heavyside Function.

Last edited: May 9, 2010
3. smarch Thread Starter Active Member

Mar 14, 2009
52
0
Hi,

I have attached another JPEG, I have come up with an expression but not sure if it is correct, I did mean to put the limits from 0 to infinity sorry about that.
However, when i put this into matlab to plot the X(f), i just comes out wrong.

File size:
30.1 KB
Views:
14
4. t_n_k AAC Fanatic!

Mar 6, 2009
5,448
782
This is my method ...

File size:
59.5 KB
Views:
15