# More Fourier Series (and differential equations)Watch

#1
I have the equation:

where

I'm asked to solve this equation using FTs.

Let Y(k) be the FT of y(x). Then, we have:

as the ft of is and the ft of f(x) is .

I rearranged this to:

The next step is to expand both the above fractions with partial fractions so I can get recognisable functions which can be fourier transformed one more time to find y(x). But I've never been good at partial fractions at all, and I'm not quite sure how to split these.

The answer is in the spoiler below...
Spoiler:
Show

for

for x < 0.

Lots and lots of thanks for any help!
0
7 years ago
#2
(Original post by trm90)
Which bit of the partial fractions are you stuck on?

If you expand the denominator you should find that it factorises nicely which then makes it quite easy to get the partial fractions.
0
7 years ago
#3
There's some stuff missing from what you've posted.

The general solution of is . (when alpha isn't 1 or -1). So why don't you have any arbitrary constants?

Also, the Fourier Transform of is undefined.
0
#4
D'oh, looks like I actually just solved it; thought I couldn't do the partial fractions properly. Thanks anyway for the posts guys!

P.S. @DFranklin I (once again) forgot to specify that it was actually f(x) = H(x)exp(-ax), sorry
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Cardiff Metropolitan University
Sat, 27 Apr '19
• University of East Anglia
Could you inspire the next generation? Find out more about becoming a Primary teacher with UEA… Postgraduate
Sat, 27 Apr '19
• Anglia Ruskin University
Health, Education, Medicine and Social Care; Arts, Humanities and Social Sciences; Business and Law; Science and Engineering Undergraduate
Sat, 27 Apr '19

### Poll

Join the discussion

#### Have you registered to vote?

Yes! (524)
37.59%
No - but I will (109)
7.82%
No - I don't want to (96)
6.89%
No - I can't vote (<18, not in UK, etc) (665)
47.7%