fft {base}

R Documentation

Discrete Fourier Transform

Usage

fft(z, inverse = FALSE)
mvfft(z, inverse = FALSE)

Arguments

z	a real or complex value array containing the values to be transformed
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

When z is a vector, the value computed and returned by fft is the univariate Fourier transform of the sequence of values in z. When z contains an array, fft computes and returns the multivariate (spatial) transform.

By contrast, mvfft takes a real or complex matrix as argument, and returns a similar shaped matrix, but with each column replaced by its discrete Fourier transform. This is useful for analyzing vector-valued series.

The FFT is fastest when the length of of the series being transformed 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

plot(fft(c(9:0,0:13, numeric(301))), type = "l")
periodogram <- function(x) { # simple periodogram
  n <- length(x)
  Mod(fft(unclass(x)))[1:(n%/%2 + 1)]^2 / (2*pi*n)
}
data(sunspots)
plot(10*log10(periodogram(sunspots)), type = "b", col = "blue")

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