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Re: Fast Fourier Transforms
*To*: mathgroup at smc.vnet.net
*Subject*: [mg21684] Re: Fast Fourier Transforms
*From*: "Mariusz Jankowski" <mjkcc at usm.maine.edu>
*Date*: Fri, 21 Jan 2000 04:00:43 -0500 (EST)
*Organization*: University of Southern Maine
*References*: <85p7u3$6je@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Charles,
Randy was mostly correct, but omitted to mention that the complex Fourier
domain has complex conjugate symmetry. Only the first N/2 (N even) Fourier
coefficients of a real signal are unique. The remaining are "negative"
frequency coefficients (you probably don't need to understand this). So, for
any real signal x, do the following
In[1]:=
Drop[Fourier[x], -Length[x]/2]
or more commonly,
In[6]:=
Drop[Abs[Fourier[x]], -Length[x]/2]
since most of the time we are interested in the magnitude of the Fourier
coefficients, only.
The remaining N/2 coefficients are organized as follows {position, frequency
in Hertz}:
{{1, 0}, {2, 1/T}, {3, 2/T}, {4, 3/T}, ... , {N/2-1, (N/2-2)/T}, {N/2,
(N/2-1)/T}
where T is the time interval between samples. 1/T is the so-called sampling
rate.
If you need more details consult any electrical engineering textbook that
has a discussion of the discrete Fourier transform (DFT).
Hope this helps,
Mariusz
======================================================
Mariusz Jankowski
University of Southern Maine
mjkcc at usm.maine.edu
"Burton" <Ctheurer at ecs.umass.edu> wrote in message
news:85p7u3$6je at smc.vnet.net...
> Hello,
> I am doing some analysis of acoustic data obtained from a pickup
located
> on a machine. The data is in the form of ordered pairs i.e. Time and
> voltage. As far as I know fft in Mathematica only operates on a list of
> single numbers. I have imported the voltage data (since the time is
simply
> incremental) and performed an fft on that successfully. My problem lays
in
> interpreting this data. I don't understand how to scale the x-axis of the
> fft plot to represent frequency.
> Any suggestions would be appreciated.
>
>
> Thanks
>
> -Charles Burton Theurer
> ctheurer at ecs.umass.edu
>
> University Of Massachusetts
>
>
>
>
>
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