ASN4 - Fourier Transform property: Parseval's Theorem: Difference between revisions
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<math>\int_{- \infty}^{\infty} (|s(t)|)^2 dt</math> in time transforms to <math>\int_{- \infty}^{\infty} (|S(f)|)^2 df</math> in frequency |
<math>\int_{- \infty}^{\infty} (|s(t)|)^2 dt</math> in time transforms to <math>\int_{- \infty}^{\infty} (|S(f)|)^2 df</math> in frequency |
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First find the magnitude of <math>s(t)</math> which is also the Inverse Fourier Transform of <math>S(f)</math>. |
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<math> |s(t)|= F ^{-1}[S(f)]=|S(f)e^{j 2 \pi f t} df | </math> |
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Since <math> |e^{j 2 \pi f t}|= \sqrt{cos^2(2 \pi f t) + sin^2(2 \pi f t)}=1 </math> |
Revision as of 01:56, 30 November 2009
Parseval's Theorem
in time transforms to in frequency
First find the magnitude of which is also the Inverse Fourier Transform of .
Since