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Discrete Fourier Transform
Syntax
fft(x, y=rep(0,length(x)), inverse=F)
Arguments
x,y
|
vectors giving the real and imaginary parts of the
sequence to be tranformed.
|
inverse
|
if TRUE, the inverse transform is computed
(the inverse has a + in the exponent of e and
divides the values by 1/length(x) before transforming).
|
Value
The the discrete Fourier transform of the values in x and y,
return as a list containing components
x, and y which give the real and imaginary parts of
the transform.
The FFT is fastest when the length of x is highly composite
(i.e. has many factors).
If this is not the case, the transform may take a long time
to compute and will use a large amount of memory.
References
Singleton, R. C. (1979).
Mixed Radix Fast Fourier Transforms,
in Programs for Digital Signal Processing,
IEEE Digital Signal Processing Committee eds.
IEEE Press.
See Also
convolve, nextn.
Examples
<![CDATA[# compute the periodogram the long way
x <- rnorm(1000)
z <- fft(x)
Ixx <- (z$x^2+z$y^2)/(2*pi*length(x))
]]>