NAME · USAGE · PARAMETERS · DESCRIPTION · BUGS
fft1d -- One dimensional Fast Fourier Transform
fft1d input output
- input
- Input image or file list. Any file template or image template can be used.
Images should be one dimensional.
- output
- Output image or file list. Any file template or image template can be used.
If the output list is shorter than the input list, the task will abort with
an error message after processing the last file or image in the input list.
- type = "complex"
- Transformation type. The possible types are real
for a real
transformation, and complex
for a complex transformation.
- format = "plain"
- Output format. The possible formats are plain
for the untouched output,
modulus
for the transformation modulus, and power
for the square
of the transformation (power spectrum).
- inverse = no
- Take inverse transformation ?
- flip = no
- Flip negative and positive parts of the transformation ?
Normaly, the FFT algorithm leaves the negative part of the transformation
at the right side of the positive part. With this parameter it's possible
to flip both parts, leaving them in a natural order.
- interval = INDEF
- Interval between data points. This parameter specifies the spacing between
data points in the input file. If this parameter has a defined value the
task will output the transformed spacing along with the transformation
values. This parameter is used only with text files.
- valkey = "CRVAL1"
- Starting value keyword. This is the name of the image header keyword used
to get the physical coordinate value of the first pixel in the input image.
- intkey = "CDELT1"
- Interval keyword. This is the name of the image header keyword used to get
the pixel coordinate spacing between pixels in the input image.
- angular = no
- Show angular frequencies ? If this parameter is set to yes
, then the
output frequencies are multiplied by two times PI. This parameter has effect
only if the interval
parameter has a defined value.
For each image or file in the input list, the task takes the direct or
inverse Fast Fourier Transform of it, and places the output in the
corresponding file or image specified in the output list.
Input files can be text files with one (real part) or two columns (real
and imaginary parts), or one-dimensional images (real or complex).
This task is a front end to some of the FFT routines provided in the IRAF
VOPS (Vector Operations). The input and output data types used by the
routines depend on the value of the real
and inverse
parameters,
acording to the following table:
real | inverse | input | output | routine
-------+---------+---------+---------+---------
no | no | complex | complex | afftrx
no | yes | complex | complex | aiftrx
yes | no | real | complex | afftxx
yes | yes | complex | real | aiftxx
If complex data is supplied and a real transformation is specified, then
the imaginary part is not used. Note that a real inverse transformation
will give complex numbers with it's imaginary part set to zero instead of
actual real numbers.
The number of lines in the output file is equal to the first power of two
greater or equal to the number of lines in the input file. Also, the number
of pixels in the output image is equal to the first power of two
greater or equal to the number of lines in the input image.
Therefore, there is no way to get exactly the original data when taking
the inverse transformatiom of a transformation. This problem can be solved
easily by just dropping the tail of the inverse transformation.
For text files the spacing between data points is specified with the
interval
parameter.
If interval
has a defined value, then the output file will have an
extra column (the first one) with the frequency values.
Otherwise only the transformation values will be written.
Note that the first column will be written even when taking the inverse
transformation, but the task won't work if it's present in the input
(see the limitations below).
For images the spacing between input pixels is taken from the the
input image header, using the keyword specified in the intkey
parameter. The physical coordinate of the first pixel is also required,
and must be specified in the valkey
parameter.
When taking a direct transformation the physical coordinate of the first
pixel is always set to the new starting value, and it's original value
is stored in the auxiliary header keyword FFT1DVAL
. When the
inverse transformation is applied the physical coordinate of the first
pixel is set back to this value.
When the spacing is specified the frequencies in the output file or image
make sense only up to the Nyquist frequency, unless the flip
parameter
is set to yes
.
This is because the FFT algorithm puts the negative part of the transformation
before the positive part of it.
If the output file or image has N points then the Nyquist frequency is
located at (N / 2 + 1) if flip
is set to no
, and at N if
flip
is set to yes
.
The default settings of the parameters are such that it is possible to take
the inverse transformation of the output of the task, and get the original
data, except for some rounding errors and the power of two limitation.
This is NOT
true under the following conditions:
- (1)
- For files or images if the type
parameter is set to real
.
- (2)
- For files or images if the format
parameter is NOT set to plain
.
- (3)
- For files or images if the flip
parameter is set to yes
.
- (4)
- For files if the interval
parameter is defined, unless the first
column of the transformation is removed.
For some unknown reason this task does not work in pipes, although it is
intended to work in them.
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This file last updated on 2 Sep 1991