Talk:Gaussian function

From Wikipedia, the free encyclopedia

Contents

[edit] FWHM

Someone should write something relating the gaussian full width half maximum to the given parameters. That way, using the fact that its a gaussian function and given the FWHM, I could construct one that works.

[edit]

Do we mean to say that

gaussian functions are eigenfunctions of the Fourier transform,

or that

eigenfunctions of the Fourier transform are gaussian functions

or neither? -- Miguel

Not all eigenfunctions of the Fourier transform are Gaussian. See Hermite polynomials. Michael Hardy 15:10, 30 Aug 2003 (UTC)

[edit] maximum entropy

Could someone add something about Gaussian functions being the ones with maximum entropy? I think this can also be related to the Heisenberg uncertainty principle since momentum and position are canonical conjugate variables.

This article links to normal distribution, which I suspect already gives that information. For non-normalized Gaussian functions, I'm not sure at this moment what the maximum-entropy statement would say. Michael Hardy 23:46, 27 Feb 2005 (UTC)

[edit] image

are they all the same bell-shape? if so, let's get a picture! - Omegatron 17:51, Mar 15, 2005 (UTC)

[edit] Definition of μ,σ

The function definition uses a,b,c as parameters, while the graph uses μ,σ as parameters. What is the relation between the two sets of parameters?

--NeilenMarais 20:18, 24 May 2006 (UTC)

Answering myself, it seems from looking at Gaussian function that a=\frac{1}{\sigma\sqrt{2\pi}}, b = μ and c=\sqrt{2}\sigma. One could mention this, or perhaps even better, generate an image using the correct parameters. Opinions? --NeilenMarais 20:27, 24 May 2006 (UTC)

Not entirely correct. Not all Gaussian functions are probability density functions, so a need not be a normalizing constant that makes the integral equal to 1.

But certainly I think the caption should explain the notation used in the illustration. Michael Hardy 21:29, 24 May 2006 (UTC)


Yes, I'd also like a better explanation of this. And also, for the 2D case, σx and σy are said to be the "spread" of the function, which term is not explained. Is it related to the FWHM?

213.115.59.220 08:49, 17 July 2007 (UTC)

[edit] Gaussian Function ..

Would I be correct if i said that a gaussian function as such represents the values a variable can have .............that is to say ......it gives us a range of possible values of the variable , or it shows the region were the value of that variable lies ......

Is that what the Gaussian function does ... —The preceding unsigned comment was added by Hari krishnan07 (talk • contribs) 04:36, 3 December 2006 (UTC).

Not directly. The gaussian function is the name for a function with specific properties e.g. as illustrated in the curves in the article. What you refer to is a probability distribution and can have the form of a gaussian Kghose 16:01, 16 December 2006 (UTC)


A function of the form f(x,a)=x^{2m}e^{-ax^{2}} are some kind of Gaussian functions?? --Karl-H 11:12, 27 January 2007 (UTC)

I think not. This is related to Gaussian functions of course, but a true Gaussian function should not have the x^{2m} term in front. Oleg Alexandrov (talk) 18:41, 27 January 2007 (UTC)

Ambiguity or error in definition of sigma?

There seems to be an ambiguity or error in the definition of sigma here. If I am not mis-informed, sigma-x and sigma-y are the standard deviations of the function along the x and y axis respectively? If this is correct, then if a 2-d Gaussian ellipse is inclined at theta = 45 degrees it would have the same sigma-x and sigma-y as a circular 2-d Gaussian, but with the covariance = 0 for the circular Gaussian and non-zero for the elliptical Gaussian.

In the 3 plots showing rotation of the ellipse from theta = 0 to theta = pi/3, the values for sigma-x and sigma-y are the same, 1 and 2 respectively. This implies that here sigma-x and sigma-y are the standard deviations along the minor and major axis of the ellipse, not along the x and y axis of the function.

Could someone please clear this up? Also, an equation that relates the angle theta to the covariance term would be helpful.

""""jgreen —Preceding unsigned comment added by 75.75.90.207 (talk) 21:22, 20 September 2007 (UTC)

Is there a spurious factor of two infront of 'b' for the 2D gaussian? The Matlab code contains no 2, whilst the latek image of the equation does. —Preceding unsigned comment added by 220.239.69.107 (talk) 05:52, 16 October 2007 (UTC)