ASN6c - Fourier Transform property: Value at origin: Difference between revisions

Revision as of 13:30, 19 December 2009

This Fourier Transform property says $s(0)$ transforms to $\int _{-\infty }^{\infty }S(f)df$

$s(0)=s(t)|_{t=0}={\mathcal {F}}^{(}-1)\left[S(f)\right]$

$s(0)=s(t)|_{t=0}=\int _{-\infty }^{\infty }S(f)e^{j2\pi (0)t}dt=\int _{-\infty }^{\infty }S(f)df$

The result is $s(0)$ transforms to $\int _{-\infty }^{\infty }S(f)df$

@@ Line 5: / Line 5: @@
 This Fourier Transform property says <math>s(0)</math> transforms to <math>\int_{-\infty}^{\infty} S(f) df</math>
-<math>s(0)= s(t)|_{t=0} = \int_{-\infty}^{\infty} S(f)e^{ j 2 \pi (0) t} dt = \int_{-\infty}^{\infty} S(f) df</math>
+<math>s(0)= s(t)|_{t=0} = \mathcal{F}^(-1)\left[S(f) \right]</math>
 <math>s(0)= s(t)|_{t=0} = \int_{-\infty}^{\infty} S(f)e^{ j 2 \pi (0) t} dt = \int_{-\infty}^{\infty} S(f) df</math>