[R] FFT (fast fourier transform) function

[mike olsen]

I'm having trouble with the fast fourier transform function ("fft").  Apparently, I'm not understanding what R's function is actually doing, let me show you with the example in the R manual:

if I put in:

    y <- 1:4
    fft(x)

i'll get this back:

10+0i    -2+2i    -2+0i    -2-2i

this is what I'm assuming:

R is interpreting the increasing values of y to have an associated value that is incremented as x increases (a plot will show y against an index, so in this case we have something like y=x over the interval 1 to 4).
The real value returned represents the coeffient of the cosine value, the imaginary value that of the sine, for n=0 to N-1 where N is the number of data points and n is the coeffient inside the sine/cosine terms, so that the output would be interpreted as:

10 - 2 cos(2 pi*x) + 2 sin (2 pi * x) -2 cos (4 pi * x) -2 cos(6 pi * x) - 2 sin (6 pi * x)

which looks nothing like y=x over the interval (1,4).

Basically, I want to be able to fit fast fourier transforms to several sets of empirical data. Controlling the period would also be important here, and the R function does not seem to have a way of handling that.  I would appreciate any information on what this function is actually doing, or information on other R packages that are able to do transforms.

Thank you for taking the time to look at this,

Michael Olsen
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