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] ?

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

==== [MESSAGE SEPARATOR] ====

```

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