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abstracted
 3 years ago
Fourier transform question:
My professor has been using this equation for the fourier transform:\[F[f(\xi)]=\int\limits_{\infty}^{\infty}f(x)e^{i \xi x}dx\]
But I have a book that claims this is the fourier transform:
\[F[f(\xi)]=\frac{1}{\sqrt{2 \pi}}\int\limits_{\infty}^{\infty}f(x)e^{i \xi x}dx\]
So........ what's with the 1/sqrt(2 pi)?
For context, this is a PDE class.
abstracted
 3 years ago
Fourier transform question: My professor has been using this equation for the fourier transform:\[F[f(\xi)]=\int\limits_{\infty}^{\infty}f(x)e^{i \xi x}dx\] But I have a book that claims this is the fourier transform: \[F[f(\xi)]=\frac{1}{\sqrt{2 \pi}}\int\limits_{\infty}^{\infty}f(x)e^{i \xi x}dx\] So........ what's with the 1/sqrt(2 pi)? For context, this is a PDE class.

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colorful
 3 years ago
Best ResponseYou've already chosen the best response.0I see a confusion about the fourier transform for angular and ordinary frequency http://en.wikipedia.org/wiki/Fourier_transform#Functional_relationships

ash2326
 3 years ago
Best ResponseYou've already chosen the best response.0@abstracted both are correct, some books use \(2\pi\) with the fourier transform and some use it with inverse fourier transform. Important thing is to use \(2\pi\) only with one of them
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