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Fourier transform: Difference between revisions
→Properties
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'''Parseval's Theorem'''<br> | '''Parseval's Theorem'''<br> | ||
<math>\int |f(x)|^2 dx = \int |F(s)|^2 ds</math> | <math>\int |f(x)|^2 dx = \int |F(s)|^2 ds</math> | ||
See [[Wikipedia: Parseval's theorem]]<br> | See [[Wikipedia: Parseval's theorem]]<br> | ||
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'''Autocorrelation'''<br> | '''Autocorrelation'''<br> | ||
<math>\int f(x') f^*(x' - x) dx' \Leftrightarrow |F(x)|^2</math> | <math>\int f(x') f^*(x' - x) dx' \Leftrightarrow |F(x)|^2</math> | ||
This is a case of the convolution theorem. | This is a case of the convolution theorem. | ||