Can anyone help me with this Fourier Transfrom question? Watch

ajxkaezj
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The Fourier transform of exp (−(x)^2/2(a)^2) is exp (−(a)^2(k)^2/2) (ignoring constants).Hence show that the convolution of exp (−(x)^2/2(a)^2) with exp (−(x)2/2(b)^2) is exp(−(x)^2/2(a^2+b^2)
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mqb2766
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(Original post by ajxkaezj)
The Fourier transform of exp (−(x)^2/2(a)^2) is exp (−(a)^2(k)^2/2) (ignoring constants).Hence show that the convolution of exp (−(x)^2/2(a)^2) with exp (−(x)2/2(b)^2) is exp(−(x)^2/2(a^2+b^2)
convolution becomes multiplication in the fourier domain.
If you can assume that result, its 2 lines.
If you have to prove from first principlies its a bit of integral swapping and variable transformation, but not too hard.
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ajxkaezj
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(Original post by mqb2766)
convolution becomes multiplication in the fourier domain.
If you can assume that result, its 2 lines.
If you have to prove from first principlies its a bit of integral swapping and variable transformation, but not too hard.
Might need a bit more info than that...
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RDKGames
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(Original post by ajxkaezj)
Might need a bit more info than that...
Are you familiar with this? https://en.wikipedia.org/wiki/Convolution_theorem
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ajxkaezj
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(Original post by RDKGames)
Are you familiar with this? https://en.wikipedia.org/wiki/Convolution_theorem
No, I shall have a closer look in the morning. Will I be able to figure out the answer from the stuff on that page?
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ajxkaezj
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(Original post by RDKGames)
Are you familiar with this? https://en.wikipedia.org/wiki/Convolution_theorem
actually I've read it and I sort of understand it but can't see how to use the information I'm given to arrive at the answer
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mqb2766
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(Original post by ajxkaezj)
Might need a bit more info than that...
What have you covered? As rdkgames shows, its just multiplying the two exponentials (fourier transforms) together.
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mqb2766
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(Original post by ajxkaezj)
actually I've read it and I sort of understand it but can't see how to use the information I'm given to arrive at the answer
1. Take the fourier transform of both signals
2. Multiply the two fourier transforms
3. Take the inverse fourier transform of the convolved (multiplied) signal - this very similar to the first step

What have you done?
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