FFT (fast fourier transform) function

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.