wavethresh (version 4.7.3)

rfft: Real Fast Fourier transform

Description

Compute a real Fast Fourier transform of x.

Usage

rfft(x)

Value

Returns the Fourier coefficients

Arguments

x

The vector whose Fourier transform you wish to take

Author

Bernard Silverman

Details

Given a vector x this function computes the real continuous Fourier transform of x, i.e. it regards x as points on a periodic function on [0,1] starting at 0, and finding the coefficients of the functions 1, \(\sqrt{2}\cos(2\pi t)\), \(\sqrt{2}\sin(2\pi t)\), etc. that gives the expansion of the interpolant of x. The number of terms in the expansion is the length of x. If x is of even length, the last coefficient will be that of a cosine term with no matching sine.

See Also

LocalSpec.wd, rfftinv

Examples

x <- seq(from=0, to=2*pi, length=150)
s1 <- sin(10*x)
s2 <- sin(7*x)
s <- s1 + s2
w <- rfft(s)
if (FALSE) ts.plot(w)
#
# Should see two peaks, corresponding to the two sines at different frequencies
#