Re: Gaussian distribution
- From: "porky_pig_jr@xxxxxxxxxxx" <porky_pig_jr@xxxxxxxxxxx>
- Date: 22 Mar 2007 14:54:08 -0700
On Mar 22, 5:34 pm, Kaba <REkalleMOunderscoreVErutane...@xxxxxxxxxxx>
wrote:
Hello
How do you prove that a Gaussian distribution integrates to 1 over -oo..
+oo?
That aside, I'm trying to find the fourier transform of a Gaussian
distribution, how do you do that?
My problems lie in the term of the form e^(bx^2) which I can't seem to
be able to integrate. I tried a change of variables x(u) = sqrt(u),
didn't take me anywhere. I also tried integration by parts two times
sequentially, didn't also take me anywhere.
This is not homework. I'd like to know the frequency response of a
Gaussian filter so I can design them using a desired cutoff frequency.
--
Kalle Rutanenhttp://kaba.hilvi.org
Integrating the gaussian function is a bit tricky, unmotivated,
probably not posssible with a standard 'single integral' integration
techniques. It is normally done with double integrals. Many calculus
textbooks contain this example (in the 'multivariable calculus' part).
In addition, any standard textbook on probability contains the same
derivation. (I believe, S. Ross "Intro to Probability" has one).
Regarding Fourier transform transforms gaussian to another gaussian,
kind of neat. Again, the actual transform derivation is widely
available.
.
- References:
- Gaussian distribution
- From: Kaba
- Gaussian distribution
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