ASN6c fixing: Difference between revisions

Latest revision as of 13:09, 19 December 2009

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

$s (0) = S (f) |_{f = 0} = \int_{- \infty}^{\infty} s (t) e^{- j 2 π (0) t} d t = \int_{- \infty}^{\infty} s (t) d t$

And $\int_{- \infty}^{\infty} s (t) d t$ in time transforms in frequency to $\int_{- \infty}^{\infty} S (f) d f$

The result is $s (0)$ transforms to $\int_{- \infty}^{\infty} S (f) d f$

@@ 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 = \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>
-The result is <math>s(0)</math> transforms to <math>\int_{-\infty}^{\infty} S(f) df</math>
+The result is <math>s(0)\!</math> transforms to <math>\int_{-\infty}^{\infty} S(f) df</math>