Package 'fftwtools'

Compute fft using fftw3

Description

These functions compute the FFT using the FFTW3 libraries. Use fftw_r2c(x, HermConj=0) for real to complex fft. This will return the result without the redundant complex conjugate. This follows the R convention for returning the unscaled inverse of the FFT. The function fftw_c2r(res, HermConj=0, n=length(x)) will invert the FFT from the result not containing the redundant complex conjugate. You must specify, n, the dimension of the original data–length–if the redundant complex conjugate is not included.

Usage

fftw(data, inverse=0, HermConj=1, n=NULL)
fftw(data, inverse=0, HermConj=1, n=NULL)
fftw_r2c(data, HermConj=1)
fftw_c2c(data, inverse=0)
fftw_c2r(data, HermConj=1, n=NULL)

Arguments

data	(complex or real) vector to be processed
inverse	(integer) 1 or 0 indicating if inverse FFT is preformed. The return follows the format of the R FFT commands–the output is not scaled.
HermConj	(integer) 1 or 0 indicating if either "Hermitian" redundant conjugate should be returned, or that the complex to real data includes the "Hermitian" redundant conjugate.
n	(integer) column length of the original data set. This is required when using the inverse complex to real FFT without providing the "Hermitian" redundant conjugate.

Author(s)

Karim Rahim

Examples

res <- fftw_r2c(1:9)
res
fftw_c2r(res)/9
res
fftw_c2r(res)/9

res <- fftw_r2c(1:10)
res
fftw_c2r(res)/10
res
fftw_c2r(res)/10

res <- fftw_r2c(1:9, HermConj=0)
res
fftw_c2r(res, HermConj=0, n=9)/9

res <- fftw_r2c(1:10, HermConj=0)
res
fftw_c2r(res, HermConj=0, n=10)/10

fftw_r2c(1:3)
fftw_c2r(fftw_r2c(1:3))/3
fftw_c2r(fftw_r2c(1:2))/2
fftw_c2r(fftw_r2c(1:4))/4


fftw_r2c(1:3, HermConj=1)
fftw_c2r(fftw_r2c(1:3, HermConj=0), HermConj=0, n=3)/3

fftw_c2r(fftw_r2c(1:4, HermConj=0), HermConj=0, n=4)/4
fftw_c2r(fftw_r2c(1:20, HermConj=0), HermConj=0, n=20)/20

---

Compute a two-dimensional FFT on a matrix using FFTW3

Description

Computes two-dimensional FFT on a matrix using the FFTW3 libraries. Use fftw_r2c_2d(x, HermConj=0) for real to complex FFT. This will return the result without the "Hermitian" redundancy. These functions follow the R convention when returning the inverse of the FFT. For the two-dimension fft, the inverse is currently requires the entire matrix, including the redundant complex conjugate.

The function fftw_c2c_xd can calculate a higher dimensional FFT on a higher dimensional array.

Usage

fftw2d(data, inverse=0, HermConj=1)
fftw_r2c_2d(data, HermConj=1)
fftw_c2c_2d(data, inverse=0)
fftw_c2c_xd(data, inverse=0)

Arguments

data	(complex or real) matrix to be processed (or array for fftw_c2c_xd)
inverse	(integer) 1 or 0 indicating if inverse FFT is preformed. The return follows the format of the R FFT commands–the output is not scaled.
HermConj	(integer) 1 or 0 indicating if either "Hermitian" redundant conjugate should be returned.

Author(s)

Karim Rahim and Ege Rubak

Examples

x=c(1, 2, 3, 9, 8, 5, 1, 2, 9, 8, 7, 2)
x= t(matrix(x, nrow=4))
mvfft(x)
t(mvfft(t(mvfft(x))))
fftw2d(x)
fftw2d(x, HermConj=0)

fftw2d(fftw2d(x), inverse=1)/12
fftw2d(fftw2d(t(x)), inverse=1)/12
fftw_r2c_2d(x)
fftw_r2c_2d(x, HermConj=0)

fftw_c2c_xd(x)

---

Compute a two-dimensional FFT on a matrix using FFTW3

Description

Computes three-dimensional FFT on an array using the FFTW3 libraries. Use fftw_r2c_3d(x, HermConj=0) for real to complex FFT. This will return the result without the "Hermitian" redundancy. These functions follow the R convention when returning the inverse of the FFT. For the two-dimension fft, the inverse is currently requires the entire matrix, including the redundant complex conjugate.

Usage

fftw3d(data, inverse=0, HermConj=1)
fftw_r2c_3d(data, HermConj=1)
fftw_c2c_3d(data, inverse=0)

Arguments

data	(complex or real) 3-dimensional array to be processed
inverse	(integer) 1 or 0 indicating if inverse FFT is preformed. The return follows the format of the R FFT commands–the output is not scaled.
HermConj	(integer) 1 or 0 indicating if either "Hermitian" redundant conjugate should be returned.

Author(s)

Karim Rahim

Examples

x=c(1, 2, 3, 9, 8, 5, 1, 2, 9, 8, 7, 2)
x= array(x, dim=c(3,2,2))

fftw3d(x)
fftw3d(x, HermConj=0)

fftw3d(fftw3d(x), inverse=1)/12

fftw_r2c_3d(x)
fftw_r2c_3d(x, HermConj=0)

---

Compute the FFT on each column of a matrix using FFTW3

Description

This will compute the FFT of each column of a matrix using the FFTW3 libraries. Use mvfftw_r2c(x, HermConj=0) for real to complex fft. This will return the result without the redundant complex conjugate. This follows the R convention for returning the unscaled inverse of the FFT. The function mvfftw_c2r(res, HermConj=0, n=dim(x)[1]) will invert the FFT from the result not containing the "Hermitian" redundant conjugate. You must specify, n, the column dimension of the original data–the column length of the original data–if the redundant complex conjugate is not included.

Usage

mvfftw(data, inverse=0, HermConj=1, n=NULL, fftplanopt=0)
mvfftw(data, inverse=0, HermConj=1, n=NULL, fftplanopt=0)
mvfftw_r2c(data, HermConj=1, fftplanopt=0)
mvfftw_c2c(data, inverse=0, fftplanopt=0)
mvfftw_c2r(data, HermConj=1, n=NULL, fftplanopt=0)

Arguments

data	(complex or real) matrix of columns to be processed
inverse	(integer) 1 or 0 indicating if inverse fft is preformed. The return follows the format of the R FFT commands. The result is not scaled.
HermConj	(integer) 1 or 0 indicating if either "Hermitian" redundant conjugate should be returned, or that the complex to real data includes the "Hermitian" redundant conjugate.
n	(integer) column length of the original data set, when using the inverse coplex to real fft without providing the "Hermitian" redundant conjugate.
fftplanopt	(integer) 0 or 1 specifying the flag passed to FFTW. 0 indicates the flag FFTW_ESTIMATE is used, and 1 indicates FFTW_MEASURE is used. See FFTW documentation for use of these flags.

Author(s)

Karim Rahim

Examples

x=c(1, 2, 3, 9, 8, 5, 1, 2, 9, 8, 7, 2)
x= t(matrix(x, nrow=4))
mvfft(x)
t(mvfft(t(mvfft(x))))

res <- mvfftw_r2c(x, HermConj=1)
res
mvfftw_c2c(res, inverse=1)/3
mvfftw_c2r(res)/3

res <- mvfftw_r2c(x, HermConj=0)
res
mvfftw_c2r(res, HermConj=0, n=3)/3


mvfftw_r2c(x, HermConj=1)
mvfft(x)
res <- mvfftw_r2c(x, HermConj=0)
res
mvfftw_c2r(res, HermConj=0, n=3)/3

res <- mvfftw_r2c(t(x), HermConj=1)
res
mvfftw_c2r(res, HermConj=1)/4
res <- mvfftw_r2c(t(x), HermConj=0)
res
mvfftw_c2r(res, HermConj=0, n=4)/4


mvfftw_r2c(t(x), HermConj=1)
mvfft(t(x))

mvfftw(mvfftw(x, HermConj=0), inverse=1, HermConj=0, n=3)/3
mvfftw(mvfftw(t(x), HermConj=0), inverse=1, HermConj=0, n=4)/4
mvfftw(mvfftw(t(x), inverse=1))/4

---