anonymous
  • anonymous
need help on fourier transform immediately
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
question 1 ab c and question 3 a b c

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anonymous
  • anonymous
@pooja195 kindly
anonymous
  • anonymous
IrishBoy123
  • 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
  • IrishBoy123
you should get \[\frac{2a}{a^2 + w^2}\]
anonymous
  • anonymous
i did the first one though, sorry, i need the rest
IrishBoy123
  • 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
  • IrishBoy123
caveat, i am pretty rusty on these but i'd knock this out as integration by parts
anonymous
  • anonymous
thank you
anonymous
  • anonymous
i need step by step though pretty urgent
anonymous
  • anonymous
kindly
IrishBoy123
  • 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
  • IrishBoy123
for (c) you have this |dw:1441264946681:dw| but double check your notation that's trivial, i'd guess
IrishBoy123
  • 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
  • anonymous
thanl you so much
IrishBoy123
  • IrishBoy123
if i read the h notation correctly, (c) simplifies to \[2\int_{0}^{1} \ sin x \ dx\]
IrishBoy123
  • IrishBoy123
soz make that simplification \[\frac{-i}{\sqrt{2 \pi}} . 2\int_{0}^{1} \ sin \ \omega x \ dx\]
anonymous
  • anonymous
Just out of curiosity, what definition does your text use for the transform?
IrishBoy123
  • 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
  • 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
  • anonymous
thanks a ton
IrishBoy123
  • 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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