[R] Different results in FFT analysis

[Tim Clark]

Dear List,
I am trying to use Fast Fourier Transformation to detect cyclical trends in the 
detection of acoustically tagged animals on an array of underwater receivers.  I 
have found two different methods to plot periodograms based on FFT, but they 
give me different results.  They find the same periods in my data, which is what 
I am interested in, but they give very different values on the y-axis.  I am new 
to time series analysis, and after reading up on all the functions involved I am 
still not sure what these two methods are plotting.  I am sorry if this is more 
of a math question, but would someone please explain why the y-axis is so 
different in these two methods?  I have attached my code and reference to their 
origin, plus an example of the data I am using.
Thanks,
Tim


#One way (From Introductory Time Series Analysis with R)
       #Plot time series, correlation, and spectrum
          layout(1:2)
          spectrum(mydata, log=c("no"))
#Another way (from 
http://knol.google.com/k/suresh-emre/fast-fourier-transform-and-power/35vsnxisjn2mw/142#)

      # calculate fft of data (this gives the complex transform)
        fourier<-fft(mydata)
      # extract the power spectrum (power is sometimes referred to as 
"magnitude")
      # magnitude=sqrt(Re(fourier)*Re(fourier)+Im(fourier)*Im(fourier))
        magnitude<-Mod(fourier)
      # extract the phase which is atan(Im(fourier)/Re(fourier))
        phase<-Arg(fourier)
      # select only first half of vectors
        magnitude_firsthalf <- magnitude[1:(length(magnitude)/2)]
        phase_firsthalf<-phase[1:(length(magnitude)/2)]
      # generate x-axis
        x.axis <- 1:length(magnitude_firsthalf)/length(magnitude)
      # plot the power spectrum
        plot(x=x.axis,y=magnitude_firsthalf,type="l")
      #Display period of major peaks
        x<-x.axis
        y<-magnitude_firsthalf
        tt<-1/x
        xyt<-data.frame(x,y,tt)
        xyt<-xyt[order(xyt$y, decreasing=TRUE),]
        head(xyt)

mydata <-
c(2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 23, 20, 0, 5, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 21, 43, 12, 2, 7, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 7, 17, 26, 5, 3, 7, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 1, 2, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 34, 25, 7, 7,
3, 6, 3, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 40, 28,
22, 11, 1, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1)

Tim Clark

Marine Ecologist
National Park of American Samoa
Pago Pago, AS  96799