- anonymous

need help on fourier transform immediately

- katieb

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- anonymous

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- anonymous

- anonymous

question 1 ab c and question 3 a b c

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- anonymous

@pooja195 kindly

- anonymous

@IrishBoy123 kindly

- IrishBoy123

for first one, look here
http://openstudy.com/users/irishboy123#/updates/55e4c101e4b0445dfd12b32e
you just need to tweak this
ie ad \(e^{-a}\) in as a constant

- IrishBoy123

you should get
\[\frac{2a}{a^2 + w^2}\]

- anonymous

i did the first one though, sorry, i need the rest

- IrishBoy123

for the next one you do
\[\frac{1}{\sqrt{2\pi}} \left[ \int_{-\infty}^{0} -x e^{-i \omega \ x} dx + \int_{0}^{1} x e^{-i \omega \ x} dx + 0 \right]\]

- IrishBoy123

caveat, i am pretty rusty on these but i'd knock this out as integration by parts

- anonymous

thank you

- anonymous

i need step by step though pretty urgent

- anonymous

kindly

- IrishBoy123

if you cannot integrate by parts i think you are going to be in trouble
especially if you are in a rush
use
\(u' = \pm x , \ v = e^{-i \omega \ x}\)

- IrishBoy123

for (c) you have this
|dw:1441264946681:dw|
but double check your notation
that's trivial, i'd guess

- IrishBoy123

for 3 you'd need to be familiar with known transforms
this kind of thing:
http://uspas.fnal.gov/materials/11ODU/FourierTransformPairs.pdf
i could read through them but if you are in a rush i would be wasting your time.... :-(

- anonymous

thanl you so much

- IrishBoy123

if i read the h notation correctly, (c) simplifies to \[2\int_{0}^{1} \ sin x \ dx\]

- IrishBoy123

soz
make that simplification
\[\frac{-i}{\sqrt{2 \pi}} . 2\int_{0}^{1} \ sin \ \omega x \ dx\]

- anonymous

Just out of curiosity, what definition does your text use for the transform?

- IrishBoy123

ah! kept meaning to bring that up
the table i linked uses
https://gyazo.com/e52ab73f1c94060a3355f9d06b0890af
as opposed to
https://gyazo.com/fa16fc59e58bc8dcc5084074a5240abf
ie the \(1/\sqrt{2 \pi }\) flavour
wolfram uses the latter also as i have checked 3a,b,c there

- IrishBoy123

here are some scribbles. in order they occur
3(a)
3(c)
3(a) done a slightly different way
3(c) not finished
issues,
1/ there may be a \(2 \pi\) or \( \sqrt{2 \pi}\) missing depending on where it sat in the definition used for the transform.
2/ i have a sign problem with 3(a), very annoying as it cropped up both times i scribbled it out. i get minus what wolfram gets each time...
3/ i can't make sense of where the delat fits in in 3(c) . it is a lot easier just doing the integral but using the tables, haven't done that in a long time.....
this might be of some help.

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- anonymous

thanks a ton

- IrishBoy123

be careful with it, i haven't done this is ages. but if you are stuck, it still might help.
good luck :p

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