Re: Fourier analysis Q
- From: "Old Man" <nomail@xxxxxxxxxx>
- Date: Fri, 4 Nov 2005 15:39:20 -0600
"Gregory L. Hansen" <glhansen@xxxxxxxxxxxxxxxxxxxxx> wrote in message
news:dkg88d$jcn$1@xxxxxxxxxxxxxxxxxxxxxxxxxxx
> In article <eMKdnfPk-qq97vfenZ2dnUVZ_tGdnZ2d@xxxxxxxxxxxxxxx>,
> Old Man <nomail@xxxxxxxxxx> wrote:
>>"bill" <please_post@xxxxxxxxxx> wrote in message
>>news:dkdb93$ohb$1@xxxxxxxxxxxxxxxxxxxx
>>>
>>> I have some data that, when I histogram it, shows some degree of
>>> quantization (i.e. the histogram has definite spikes at regular
>>> intervals, and this is not an artifact of the histogramming
>>> procedure). The spikes decay in magnitude roughly exponentially.
>>> (In between the spikes the hits are few but not zero.)
> ...
>>
>>You really have to be more specific about the physics.
>>
>>If the data represents an energy spectrum, such as that obtained
>>from nuclear inelastic scattering data, then a Fourier transform of
>>the entire spectrum isn't useful. However, a Fourier transform
>>of the histogram of an individual 'spike' will give you the decay
>>time for the nuclear excited state represented by that 'spike'.
>
> It will? I'd find the decay time by fitting an exponential to it. How
> would a Fourier transform help?
The energy width; delta_E, of a peak which represents
inelastic scattering from a nuclear excited state is related
to the state's life time, delta_t, by
delta_E * delta_t = hbar
One gets delta_E from fitting a Gaussian to the peak and
setting delta_E = 2 * sigma.
The Fourier transform of a Gaussian is another Gaussian,
such that sigma_1 * sigma_2 = 1
[Old Man]
.
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