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Re: fourier,units
*To*: mathgroup at smc.vnet.net
*Subject*: [mg4012] Re: [mg3971] fourier,units
*From*: Ralheid at aol.com
*Date*: Mon, 20 May 1996 02:12:02 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
rebscher at geo.uni-bonn.de asks
> given: f[I b] = Abs[Fourier[data]]
>now my question:
>what kind of units on the axis do I get when my
>data are of the form [V] ?
I read this as;
data = {vector}
f[I w] = Abs[Fourier[data]]
The x-axis and Y-axis units are related to the units of the data. Looking at
real values for data
Given a specific case that I frequently encounter. Having data's y_Values
represent amplitude[time], and each data point's x_Position represents a
uniform increment of time. ( say .001 second for instance) . Then, if the
dimensions of data is 1000. The data set represent f[time] , 0<=time<+1.00.
The fourier component set f[I w] then has the following units; y-values are
still amplitude, they are the real fouier component's (Sqrt[1000]
Realamplitude / 2 ). The first term is the zero order term or average
value. The first 499 terms are equal in reverse order to the last 499 terms
(the . If you plot f[I w ] using only the first 499 terms each x-value
represents an increment of circular frequency (omega), the first f[2] will be
(2 Pi radians/second (or one cycle /sec) the 499th f[50] will be (499 2 Pi)
radians /sec ( 49 cycles /sec).
To represent the correct numerical values for the fourier components the
following shows the correct values
ListPlot[2 Abs[Take[f[I w],{1,500}]]/Sqrt[1000]]
I hope the above makes sense to you
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