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 > > > > >