# Fouriers Transform

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#1
F(t)= 0 mod(t)>10
cos t -10<t<10
a)Use the fouriers integral theorem to derive the fouriers transform of F(t)
b)Use the fouriers transforms of the top-hat and cosine functions, and properties of the fouriers transform to confirm your result.
Can anyone please help me on this example. I missed the lectures due to being ill and now im struggling with it. Thank you
0
1 year ago
#2
(Original post by dilu777)
F(t)= 0 mod(t)>10
cos t -10<t<10
a)Use the fouriers integral theorem to derive the fouriers transform of F(t)
b)Use the fouriers transforms of the top-hat and cosine functions, and properties of the fouriers transform to confirm your result.
Can anyone please help me on this example. I missed the lectures due to being ill and now im struggling with it. Thank you
You have an example of a discrete (top hat) and a continuous (cos) function in there, both of them have very standard book value solutions for the FT, and you take two different mathematical approaches to them. One requires a Fourier integral, one needs a (very simple) discrete Fourier sum to do from first principles.
cos t -10<t<10 is a bit more interesting, a good way to approach it is to note that it can be viewed as an infinite cos t multiplied by a top hat mod(t)>10. Do you know how the product of two functions behaves under the FT ?

If the above does not make sense, then you really need to go back to basics and work through those lecture notes in detail as the FT (which is a wonderfully powerful tool) can take a few goes to get your head around as it has both conceptual and mathematical complexities..
0
#3
(Original post by Mr Wednesday)
You have an example of a discrete (top hat) and a continuous (cos) function in there, both of them have very standard book value solutions for the FT, and you take two different mathematical approaches to them. One requires a Fourier integral, one needs a (very simple) discrete Fourier sum to do from first principles.
cos t -10<t<10 is a bit more interesting, a good way to approach it is to note that it can be viewed as an infinite cos t multiplied by a top hat mod(t)>10. Do you know how the product of two functions behaves under the FT ?

If the above does not make sense, then you really need to go back to basics and work through those lecture notes in detail as the FT (which is a wonderfully powerful tool) can take a few goes to get your head around as it has both conceptual and mathematical complexities..fhdfd
Sorry i've been away for a while. This Fouriers transform is a topic i have no idea on how to approach. I only skimmed through the lecture notes and therefore i have to do that all over again
0
1 year ago
#4
(Original post by dilu777)
Sorry i've been away for a while. This Fouriers transform is a topic i have no idea on how to approach. I only skimmed through the lecture notes and therefore i have to do that all over again
Ok, down to you then. the FT is a really important tool so one you need to get to grips with.
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