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