dft: Discrete Fourier Transform

In obreschkow/cooltools: Practical Tools for Scientific Computations and Visualizations

Discrete Fourier Transform

Description

Discrete Fourier Transform (DFT) with longest modes at the center in Fourier space and normalized such that dft(dft(f),inverse)=f. This is the discretization scheme described in Appendix D of Obreschkow et al. 2013, ApJ 762. Relies on fft.

Usage

dft(f, inverse = FALSE, shift = -floor(dim(as.array(f))/2), simplify = TRUE)

Arguments

f	real or complex D-dimensional array containing the values to be transformed.
inverse	logical flag; if TRUE the inverse Fourier transform is performed.
shift	D-vector specifying the integer shift of the coordinates in Fourier space. Set to shift=rep(0,D) to produced a DFT with the longest mode at the corner in Fourier space.
simplify	logical flag; if TRUE the complex output array will be simplified to a real array, if it is real within the floating point accuracy

Value

Returns an array of the same shape as f, containing the (inverse) Fourier Transform.

Author(s)

Danail Obreschkow

See Also

fft

Examples

## DFT of a 2D normal Gaussian function
n = 30
f = array(0,c(n,n))
for (i in seq(n)) {
  for (j in seq(n)) f[i,j] = exp(-(i-6)^2/4-(j-8)^2/2-(i-6)*(j-8)/2)
}
plot(NA,xlim=c(0,2.1),ylim=c(0,1.1),asp=1,bty='n',xaxt='n',yaxt='n',xlab='',ylab='')
rasterImage(f,0,0,1,1,interpolate=FALSE)
g = dft(f)
img = array(hsv((pracma::angle(g)/2/pi)%%1,1,abs(g)/max(abs(g))),c(n,n))
rasterImage(img,1.1,0,2.1,1,interpolate=FALSE)
text(0.5,1,'Input function f',pos=3)
text(1.6,1,'DFT(f)',pos=3)

obreschkow/cooltools documentation built on Nov. 16, 2024, 2:46 a.m.