| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
13 Mar 2006 01:43:41 PM |
| Object: |
Need clarification of rms width definition |
Hi Folks,
I am trying to calculate the rms width in time and frequency domain of
some intensity function, for example a gaussian.
I'm a bit confused about the definition of an rms width. I've seen one
definition which says that the rms width is the variance
(sigma)^2=<t>^2 - <t^2> and another definition where it defined as the
second order moment, which is just <t^2>. Does anyone know which one
is the correct definition.
Thanks.
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| User: "PD" |
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| Title: Re: Need clarification of rms width definition |
13 Mar 2006 01:52:39 PM |
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wrote:
Hi Folks,
I am trying to calculate the rms width in time and frequency domain of
some intensity function, for example a gaussian.
I'm a bit confused about the definition of an rms width. I've seen one
definition which says that the rms width is the variance
(sigma)^2=<t>^2 - <t^2> and another definition where it defined as the
second order moment, which is just <t^2>. Does anyone know which one
is the correct definition.
Well, actually neither.
The right definition is
(sigma)^2 = <t^2> - <t>^2.
The 2nd order moment calculation simply assumes that the distribution
has been rescaled so that <t>=0 and so the 2nd term vanishes. No
biggie.
Thanks.
.
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| User: "Halm" |
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| Title: Re: Need clarification of rms width definition |
13 Mar 2006 02:32:29 PM |
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(sigma)^2=<t>^2 - <t^2> and another definition where it defined as the
second order moment, which is just <t^2>. Does anyone know which one
is the correct definition.
you get the mean value of any moment
<t^n> integral t^n*pdf (pdf= prob. dens. function)
The square of the variation of the mean value is
(delta T )^2 = <t^2> - <t>^2 (this formula is general)
for more information look at www.nist.gov seach for engineering
statistical handbook
Please be sure to understand the idea of "probability" versus a set of
values giving a mean value!
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