ASN6c - Fourier Transform property: Value at origin: Difference between revisions
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<math>s(0)= s(t)|_{t=0} = \mathcal{F}^{-1}\left[S(f) \right])|_{t=0}</math> |
<math>s(0)= s(t)|_{t=0} = \mathcal{F}^{-1}\left[S(f) \right])|_{t=0}</math> |
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Evaluating the inverse Fourier transform at time zero |
Evaluating the inverse Fourier transform at time zero |
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<math>s(0) = \int_{-\infty}^{\infty} S(f)e^{ j 2 \pi f(0) } df = \int_{-\infty}^{\infty} S(f) df</math> |
<math>s(0) = \int_{-\infty}^{\infty} S(f)e^{ j 2 \pi f(0) } df = \int_{-\infty}^{\infty} S(f) df</math> |
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Therefore this process shows that <math>s(0) \!</math> is <math>\int_{-\infty}^{\infty} S(f) df</math> |
Latest revision as of 13:40, 19 December 2009
Value at Origin
This Fourier Transform property says becomes
Evaluating the inverse Fourier transform at time zero
Therefore this process shows that is