fourier transforms question??

importunate

2

I am a bit stuck on this question... some help would be appreciated.

I think I can do a) and b)... but when I get to c I am stuck. Ill post what I have done...

Reply 1

ghostwalker

17

Original post by importunate

...

Not studied fourier transfroms, so don't know why you're doing it the way you are.

But, applying the formula from part (a), using IBP, gives the desired result, after using the hint, and multiplying top and bottom by appropriate amounts to get into the form they desire.

Reply 2

importunate

OP

2

Original post by ghostwalker

Not studied fourier transfroms, so don't know why you're doing it the way you are.

But, applying the formula from part (a), using IBP, gives the desired result, after using the hint, and multiplying top and bottom by appropriate amounts to get into the form they desire.

Sorry I get what you are saying... great. Ill just have to see if it works now... have tried doing it over plus and minus infinity and it was horrible.

(edited 13 years ago)

Reply 3

importunate

OP

2

still cant do it. some ideas would be appreciated . thanks

Reply 4

ghostwalker

17

Original post by importunate

still cant do it. some ideas would be appreciated . thanks

Well f(x) = a-x for 0<= x <= a

So you want

\displaystyle\frac{2}{\sqrt{2 \pi}}\int_0^a (a-x)cos(kx)dx

Upper limit is a, since f(x) = 0 for x>= a

(edited 13 years ago)

Reply 5

importunate

OP

2

dont you have to include the -x+a section?

Reply 6

ghostwalker

17

Original post by importunate

dont you have to include the -x+a section?

Sorry, don't understand that statement.

If you're refering to the part of the graph from -a to 0, then it seems to me that the whole point of part (a) was to show that you don't need to consider it for an even function, as is the case here.

Reply 7

importunate

OP

2

Thanks... but when I integrate this I get:

-(coa(ak)-1)*root2/(k^2*rootpi....

this isnt the answer I am looking for...

Reply 8

ghostwalker

17

Original post by importunate

Thanks... but when I integrate this I get:

-(coa(ak)-1)*root2/(k^2*rootpi....

this isnt the answer I am looking for...

That's because you haven't applied the hint and multiplied top and bottom by appropriate amounts yet to get it into the form requested. Looks OK so far....