R: Real Fast Fourier transform

rfft {wavethresh} | R Documentation

## Real Fast Fourier transform

### Description

Compute a real Fast Fourier transform of `x`.

### Usage

    rfft(x)

### Arguments

`x` | The vector whose Fourier transform you wish to take

### 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.

### Value

Returns the Fourier coefficients

### Author(s)

Bernard Silverman

### 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)
    ## Not run: ts.plot(w)
    #
    # Should see two peaks, corresponding to the two sines at different frequencies
    #

[Package wavethresh version 4.6.8 Index]