# Fouriers integral theorem

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#1
Hi so my lecturer is using this definition of fouriers integral theorem

But then when trying to explain why that makes the integral theorem a way to show that any function can be represented by an infinite sum of sin and cosine function, he writes (writing in pen not pencil)

Is there some sort of trick here I can’t see? Because if I do coswt + isinwt I get e^+iwt not e^-iwt
If I want e^-iwt I get coswt -isinwt

Any thoughts/explanations/advice would be much appreciated. Thank you!
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1 month ago
#2
(Original post by littlebitthick)
Hi so my lecturer is using this definition of fouriers integral theorem

But then when trying to explain why that makes the integral theorem a way to show that any function can be represented by an infinite sum of sin and cosine function, he writes (writing in pen not pencil)

Is there some sort of trick here I can’t see? Because if I do coswt + isinwt I get e^+iwt not e^-iwt
If I want e^-iwt I get coswt -isinwt

Any thoughts/explanations/advice would be much appreciated. Thank you!
Could you explain what your question is a bit more?
There is a simple typo (negative sign) in the second picture , but that's all? What you said in your post is correct.
There is little to do with the actual Fourier transform.

If that's your lecturers notes, typos do creep in?
Last edited by mqb2766; 1 month ago
1
#3
(Original post by mqb2766)
Could you explain what your question is a bit more?
There is a simple typo (negative sign) in the second picture , but that's all? What you said in your post is correct.
There is little to do with the actual Fourier transform.

If that's your lecturers notes, typos do creep in?
Thank you! Just assumed I was missing a trick here and didn’t think it could just be a typo!

I was thinking there must be some sort of trick because he says that it shows that ‘any function may be represented by an infinite sum of sine and cosine functions’ so thought there must be a way to make it isine + cosine
0
1 month ago
#4
(Original post by littlebitthick)
Thank you! Just assumed I was missing a trick here and didn’t think it could just be a typo!

I was thinking there must be some sort of trick because he says that it shows that ‘any function may be represented by an infinite sum of sine and cosine functions’ so thought there must be a way to make it isine + cosine
It's based on Euler identity (on the slide)
e^(ix) = cos(x) + i*sin(x)
Where the trig functions are even/odd. Simple typo that's all.
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