Name
fft - fft 2d on an image
Synopsis
fft [options] <in> <out>
Description
fft computes a Fast Fourier Transform on an input image.
fft can also compute an inverse FFT. Results can have
swapped quadrants, and can be expressed in polar or carte-
sian coordinates.
Take care about the formats : polar/cartesian and
swapped/unswapped. The default procedure is:
In input of a forward FFT, an image is required. It is
taken as the real part (in cartesian coordinates) of a
complex 2d signal which imaginary part is set to zeros.
The output of a forward FFT is a complex 2d signal, i.e. 2
image planes. By default, the output is converted to polar
coordinates (modulus, phase), and then quadrants are
swapped in both modulus and phase to put low frequencies
at the center of the images. To prevent this default
behaviour, use the -n and -c options described below.
In input of an inverse FFT, a cube containing 2 images is
required. It is taken as a complex 2d signal which first
plane contains the modulus and second plane contains the
phase. Before the inverse FFT is computed, a swapping of
quadrants occurs, and then a conversion to cartesian
(real, imaginary) coordinates is performed. To prevent
quadrant swapping or cartesian conversion, use the -n and
-c options described below.
The output of an inverse FFT is a cube containing 2 images
in cartesian unswapped format, first one being the real
part, second one being the imaginary part (meaningless
imagewise).
Algorithm
fft uses the Danielson-Lanczos lemma, in a code based on
one originally written by N. M. Brenner, described in
Numerical Recipes in C.
Options
-c Switches to cartesian mode the following data:
output for a forward FFT (default is polar), or
input for an inverse FFT.
-i Inverse FFT. The input is a cube containing two
planes only. Default I/O format for these 2 planes
is polar coordinates (modulus, phase). It will out-
put a cube containing 1 plane only (imaginary part
is meaningless imagewise). The input will be
swapped before FFT, unless the -n option is used.
-n This option prevents fft from swapping the output
of a forward FFT and the input of an inverse FFT.
Swapping is done according to the following rule :
1 2
4 3
becomes then
3 4
2 1
which puts then the lowest frequencies at the center of
the image.
Files
Input files shall all comply with FITS format.