Week of 10/29
(Difference between revisions)
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The fundamental property of the delta function: you must remember this | The fundamental property of the delta function: you must remember this | ||
− | <math>\int _ a ^ b \delta (t - t_0) f(t) dt = f(t_0)</math> if <math>t_0 \ | + | <math>\int _ a ^ b \delta (t - t_0) f(t) dt = f(t_0)</math> if <math>t_0 \in [a,b] \,</math>. Remember, you evaluate <math>f \,</math> at the point where the argument of the delta function is zero. In this case when<math> t = t_0. \,</math> |
− | <math>\int _ a ^ b \delta (t - t_0) f(t) dt = 0</math> if <math>t_0 \ | + | <math>\int _ a ^ b \delta (t - t_0) f(t) dt = 0</math> if <math>t_0 \notin [a,b] \,</math> |
Revision as of 15:16, 31 October 2007
Download FT, wavepackets, bandwidth ... |
A few examples of the importance of Gaussian distributions
Maxwell Boltzmann velocity distribution
It turns out that the FWHM is nontrivial: this link shows how to compute it
the answer turns out to be
The fundamental property of the delta function: you must remember this
if . Remember, you evaluate at the point where the argument of the delta function is zero. In this case when
if
Two nice links on Sinc functions: from Mathworld and Wikipedia
The following two figures are from Barbara Romanowicz, a seismologist at the University of California, Berkeley.
Download lecture notes from 10/31/07 |
Download Sinc function interpolation via the samping theorem |