Week of 10/29
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[http://mathworld.wolfram.com/Convolution.html very nice graphical illustration of the convolution] | [http://mathworld.wolfram.com/Convolution.html very nice graphical illustration of the convolution] | ||
+ | {{mathematica|filename=Convolution.nb|title=Creating a realistic time series by convolving a wavelet with a series of spikes}} | ||
{{mathematica|filename=Sincinterpolation.nb|title=Sinc function interpolation via the samping theorem}} | {{mathematica|filename=Sincinterpolation.nb|title=Sinc function interpolation via the samping theorem}} |
Revision as of 15:51, 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 .
if
Remember, in the former case, you evaluate at the point where the argument of the delta function is zero. In this case when
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 |
very nice graphical illustration of the convolution
Download Creating a realistic time series by convolving a wavelet with a series of spikes |
Download Sinc function interpolation via the samping theorem |