ASN6c fixing: Difference between revisions

Latest revision as of 12:09, 19 December 2009

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

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

And $\int _{-\infty }^{\infty }s(t)dt$ in time transforms in frequency to $\int _{-\infty }^{\infty }S(f)df$

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(f)|_{f=0} = [\int_{-\infty}^{\infty} s(t)e^{- j 2 \pi f t} dt]|_{f=0} = \int_{-\infty}^{\infty} s(t) dt</math>
+<math>s(0)= S(f)|_{f=0} = \int_{-\infty}^{\infty} s(t)e^{- j 2 \pi (0) t} dt = \int_{-\infty}^{\infty} s(t) dt</math>
 And <math> \int_{-\infty}^{\infty} s(t) dt</math> in time transforms in frequency to <math>\int_{-\infty}^{\infty} S(f) df</math>