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December 12th, 2011, 09:41 AM   #1
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Fourier transform and integral

I need to compute the integral


by using the following Fourier transform





1)I start with the inversion







and going back to my integral



and the result agrees with the answers

But I cannot find out how to compute this integral, could someone show me this?

also using the same Fourier transform

thank you
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December 12th, 2011, 04:48 PM   #2
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Re: Fourier transform and integral

Use





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December 13th, 2011, 12:36 AM   #3
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Re: Fourier transform and integral

thank you very much, I have been trying to solve it for hours maybe because I still do not know how did you compute this inversion of Fourier transform?

Quote:
Originally Posted by wnvl


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December 13th, 2011, 03:05 PM   #4
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Re: Fourier transform and integral

Quote:
Originally Posted by rayman
thank you very much, I have been trying to solve it for hours maybe because I still do not know how did you compute this inversion of Fourier transform?

Quote:
Originally Posted by wnvl


The invers Fourier transform of f(x)^2 is equal to the invers Fourier transform of f(x) convoluted with itself.
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January 6th, 2012, 07:38 AM   #5
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Re: Fourier transform and integral

I actually did compute the same transform and got slightly different result

Our teacher uses this formula for convolution

Do we always have this constant ??
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January 6th, 2012, 07:42 AM   #6
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Re: Fourier transform and integral

Quote:
Originally Posted by rayman
Do we always have this constant ??
That depends on your definition of Fourier transform and inverse Fourier transform.
There are different definitions in use.
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January 6th, 2012, 07:49 AM   #7
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Re: Fourier transform and integral

ah okej
that is very confusing
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