Week of 10/29

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Latest revision as of 16:30, 5 November 2007

A few examples of the importance of Gaussian distributions

It turns out that the FWHM is nontrivial: this link shows how to compute it

the answer turns out to be $2 \sqrt{2 \ln 2} \sigma \approx 2.3548 \sigma$

The fundamental property of the delta function: you must remember this

$\int _ a ^ b \delta (t - t_0) f(t) dt = f(t_0)$ if $t_0 \in [a,b] \,$ .

$\int _ a ^ b \delta (t - t_0) f(t) dt = 0$ if $t_0 \notin [a,b] \,$

Remember, in the former case, you evaluate $f \,$ at the point where the argument of the delta function is zero. In this case when $t = t_0. \,$

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.

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 [http://mathworld.wolfram.com/SincFunction.html from Mathworld] and
 [http://en.wikipedia.org/wiki/Sinc_function Wikipedia]
+{{mathematica|filename=Spectral_interferometry.nb|title=Interfering gaussians}}
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 [[Image:Slide0030.gif]]
+{{PDF|filename=10-29-07.pdf|title=lecture notes from 10/29/07}}
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 {{mathematica|filename=Convolution.nb|title=Creating a realistic time series by convolving a wavelet with a series of spikes}}
+{{PDF|filename=11-2-07.pdf|title=Optional digression on sampling theorem}}
-{{mathematica|filename=Sincinterpolation.nb|title=Sinc function interpolation via the samping theorem}}