You are Here: Home >< Maths

Fourier Transforms - power spectra watch

1. A light source starts to emit at time = 0 and the amplitude of the emission is for t > 0. Show that the power spectrum is:

As a hint, I'm told to FT the signal and then square it, which makes sense to me. But I am having trouble FTing the function they've given. As I understand it, my integral should look like

but I get totally stumped here. Any tips, anyone?
2. (Original post by trm90)
A light source starts to emit at time = 0 and the amplitude of the emission is for t > 0. Show that the power spectrum is:

As a hint, I'm told to FT the signal and then square it, which makes sense to me. But I am having trouble FTing the function they've given. As I understand it, my integral should look like

but I get totally stumped here. Any tips, anyone?
I'd start by noting that

3. (Original post by EEngWillow)
I'd start by noting that

Ye I tried putting it in that form before, but the problem is the sin(wt) term... I know that the FT of is but I don't feel I'm going to get anywhere with the trig term in there
4. 2i sin wt = exp(iwt)-exp(-iwt).
5. (Original post by DFranklin)
2i sin wt = exp(iwt)-exp(-iwt).
Brilliant - thanks very much

Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 28, 2011
The home of Results and Clearing

2,738

people online now

1,567,000

students helped last year
Today on TSR

University open days

1. Sheffield Hallam University
Tue, 21 Aug '18
2. Bournemouth University
Wed, 22 Aug '18
3. University of Buckingham
Thu, 23 Aug '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants