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Topic: Fourier Transform (Read 984 times) |
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MonicaMath
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Fourier Transform
« on: Feb 25th, 2010, 7:38am » |
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I have a question
I know that we can use the fact that (cosx)'=-sinx to find the fourier transform
for sinx on [-pi/2, pi/2] by using FT properties, But why we can't use the same idea for
(sinx)'=cosx to find the FT of cosx on [-pi/2, pi/2]
any help please
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Michael Dagg
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Re: Fourier Transform
« Reply #1 on: Feb 25th, 2010, 2:41pm » |
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I think perhaps when you speak of sin with a Fourier transform on
[-pi/2, pi/2], you mean the function s(x) which agrees with sin x on
that interval and is extended to the line so that it has period pi. And
likewise for cos . If you work with the functions with period pi , you
look for a Fourier transform (series) that looks like this:
\sum_{k=-\infty} ^ {+\infty} c_k e^{2ikx}
I don't know just how you are proceeding, so I'll not get technical but
just do the easy thing and try to make one simple remark that may help.
When two functions have the same derivative, they differ by a constant,
which may be nonzero.
Note that s(x) has average value 0 , and hence 0th Fourier coefficient
0 , whereas c(x) has a nonzero average value and a nonzero 0th Fourier
coefficient.
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| « Last Edit: Feb 25th, 2010, 2:41pm by Michael Dagg » |
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Michael Dagg
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MonicaMath
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Re: Fourier Transform
« Reply #2 on: Feb 28th, 2010, 8:31am » |
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not clear.... does anyone have another idea ?!
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Michael Dagg
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Re: Fourier Transform
« Reply #3 on: Feb 28th, 2010, 8:39pm » |
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If you can show me how you are proceeding then
I think I can make it clear. You could start off by
demonstrating your first sentence.
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Regards,
Michael Dagg
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MonicaMath
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Re: Fourier Transform
« Reply #4 on: Mar 1st, 2010, 8:59am » |
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I mean:
Is there any condition that should be satisfied on these functions so we can apply the result !? and if so, what is the condition that sinx (or cosx ) in
[-p1/2, pi/2] doesn't satisfied in this case ??
thank you
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Obob
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Re: Fourier Transform
« Reply #5 on: Mar 1st, 2010, 9:11am » |
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That didn't clarify things at all.
Are you extending the functions periodically to the whole real line?
And you should provide the argument for how to calculate the FT of sin x.
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