inttrans — FFT and other integral transforms
gint | gwy_fft_find_nice_size () |
void | gwy_data_line_fft () |
void | gwy_data_line_part_fft () |
void | gwy_data_line_fft_raw () |
void | gwy_data_field_1dfft () |
void | gwy_data_field_area_1dfft () |
void | gwy_data_field_1dfft_raw () |
void | gwy_data_field_2dfft () |
void | gwy_data_field_area_2dfft () |
void | gwy_data_field_2dfft_raw () |
void | gwy_data_field_2dfft_humanize () |
void | gwy_data_field_2dfft_dehumanize () |
void | gwy_data_field_fft_postprocess () |
void | gwy_data_field_fft_filter_1d () |
void | gwy_data_field_cwt () |
#include <libprocess/gwyprocess.h>
There are two main groups of FFT functions.
High-level functions such as gwy_data_field_2dfft()
, gwy_data_line_fft()
can perform windowing, leveling and other pre- and postprocessing.
This makes them suitable for calculation of spectral densities
and other statistical characteristics.
Low-level functions have raw
appended to their name:
gwy_data_field_2dfft_raw()
, gwy_data_line_fft_raw()
. They
perform no other operations on the data beside the transform itself.
This makes them suitable for applications where both forward and inverse
transform is performed.
Both types of functions wrap
FFTW3routines.
gint
gwy_fft_find_nice_size (gint size
);
Finds a nice-for-FFT array size.
The `nice' means three properties are guaranteed:
it is greater than or equal to size
;
it can be directly used with current FFT backend without scaling
(since 2.8 this is true for any size);
and the transform is fast, i.e. the number is highly factorable.
To be compatible with Gwyddion <= 2.7 one has to pass only data fields and lines with sizes returned by this function to raw integral transforms. Otherwise this function is mainly useful if you extend and pad the input data for other reasons and thus have the freedom to choose a convenient transform size.
size |
Transform size. |
A nice FFT array size.
void gwy_data_line_fft (GwyDataLine *rsrc
,GwyDataLine *isrc
,GwyDataLine *rdest
,GwyDataLine *idest
,GwyWindowingType windowing
,GwyTransformDirection direction
,GwyInterpolationType interpolation
,gboolean preserverms
,gint level
);
Calculates Fast Fourier Transform of a data line.
A windowing or data leveling can be applied if requested.
rsrc |
Real input data line. |
|
isrc |
Imaginary input data line. |
|
rdest |
Real output data line. It will be resized to the size of the input data line. |
|
idest |
Imaginary output data line. It will be resized to the size of the input data line. |
|
windowing |
Windowing mode. |
|
direction |
FFT direction. |
|
interpolation |
Interpolation type. Ignored since 2.8 as no resampling is performed. |
|
preserverms |
|
|
level |
0 to perform no leveling, 1 to subtract mean value, 2 to subtract line (the number can be interpreted as the first polynomial degree to keep, but only the enumerated three values are available). |
void gwy_data_line_part_fft (GwyDataLine *rsrc
,GwyDataLine *isrc
,GwyDataLine *rdest
,GwyDataLine *idest
,gint from
,gint len
,GwyWindowingType windowing
,GwyTransformDirection direction
,GwyInterpolationType interpolation
,gboolean preserverms
,gint level
);
Calculates Fast Fourier Transform of a part of a data line.
A windowing or data leveling can be applied if requested.
rsrc |
Real input data line. |
|
isrc |
Imaginary input data line. Since 2.7 it can be |
|
rdest |
Real output data line, it will be resized to |
|
idest |
Imaginary output data line, it will be resized to |
|
from |
The index in input lines to start from (inclusive). |
|
len |
Lenght of data line part, it must be at least 2. |
|
windowing |
Windowing mode. |
|
direction |
FFT direction. |
|
interpolation |
Interpolation type. Ignored since 2.8 as no resampling is performed. |
|
preserverms |
|
|
level |
0 to perform no leveling, 1 to subtract mean value, 2 to subtract line (the number can be interpreted as the first polynomial degree to keep, but only the enumerated three values are available). |
void gwy_data_line_fft_raw (GwyDataLine *rsrc
,GwyDataLine *isrc
,GwyDataLine *rdest
,GwyDataLine *idest
,GwyTransformDirection direction
);
Calculates Fast Fourier Transform of a data line.
No leveling, windowing nor scaling is performed.
The normalisation of FFT is symmetrical, so transformations in both directions are unitary.
Since 2.8 the dimensions need not to be from the set of sizes returned
by gwy_fft_find_nice_size()
.
rsrc |
Real input data line. |
|
isrc |
Imaginary input data line. Since 2.7 it can be |
|
rdest |
Real output data line. It will be resized to the size of the input data line. |
|
idest |
Imaginary output data line. It will be resized to the size of the input data line. |
|
direction |
FFT direction. |
Since: 2.1
void gwy_data_field_1dfft (GwyDataField *rin
,GwyDataField *iin
,GwyDataField *rout
,GwyDataField *iout
,GwyOrientation orientation
,GwyWindowingType windowing
,GwyTransformDirection direction
,GwyInterpolationType interpolation
,gboolean preserverms
,gint level
);
Transforms all rows or columns in a data field with Fast Fourier Transform.
If requested a windowing and/or leveling is applied to preprocess data to obtain reasonable results.
rin |
Real input data field. |
|
iin |
Imaginary input data field. It can be |
|
rout |
Real output data field, it will be resized to area size. |
|
iout |
Imaginary output data field, it will be resized to area size. |
|
orientation |
Orientation: pass |
|
windowing |
Windowing type. |
|
direction |
FFT direction. |
|
interpolation |
Interpolation type. Ignored since 2.8 as no resampling is performed. |
|
preserverms |
|
|
level |
0 to perform no leveling, 1 to subtract mean value, 2 to subtract line (the number can be interpreted as the first polynomial degree to keep, but only the enumerated three values are available). |
void gwy_data_field_area_1dfft (GwyDataField *rin
,GwyDataField *iin
,GwyDataField *rout
,GwyDataField *iout
,gint col
,gint row
,gint width
,gint height
,GwyOrientation orientation
,GwyWindowingType windowing
,GwyTransformDirection direction
,GwyInterpolationType interpolation
,gboolean preserverms
,gint level
);
Transforms all rows or columns in a rectangular part of a data field with Fast Fourier Transform.
If requested a windowing and/or leveling is applied to preprocess data to obtain reasonable results.
rin |
Real input data field. |
|
iin |
Imaginary input data field. It can be |
|
rout |
Real output data field, it will be resized to area size. |
|
iout |
Imaginary output data field, it will be resized to area size. |
|
col |
Upper-left column coordinate. |
|
row |
Upper-left row coordinate. |
|
width |
Area width (number of columns), must be at least 2 for horizontal transforms. |
|
height |
Area height (number of rows), must be at least 2 for vertical transforms. |
|
orientation |
Orientation: pass |
|
windowing |
Windowing type. |
|
direction |
FFT direction. |
|
interpolation |
Interpolation type. Ignored since 2.8 as no resampling is performed. |
|
preserverms |
|
|
level |
0 to perform no leveling, 1 to subtract mean value, 2 to subtract lines (the number can be interpreted as the first polynomial degree to keep, but only the enumerated three values are available). |
void gwy_data_field_1dfft_raw (GwyDataField *rin
,GwyDataField *iin
,GwyDataField *rout
,GwyDataField *iout
,GwyOrientation orientation
,GwyTransformDirection direction
);
Transforms all rows or columns in a data field with Fast Fourier Transform.
No leveling, windowing nor scaling is performed.
The normalisation of FFT is symmetrical, so transformations in both directions are unitary.
Since 2.8 the dimensions need not to be from the set of sizes returned
by gwy_fft_find_nice_size()
.
rin |
Real input data field. |
|
iin |
Imaginary input data field. It can be |
|
rout |
Real output data field, it will be resized to |
|
iout |
Imaginary output data field, it will be resized to |
|
orientation |
Orientation: pass |
|
direction |
FFT direction. |
Since: 2.1
void gwy_data_field_2dfft (GwyDataField *rin
,GwyDataField *iin
,GwyDataField *rout
,GwyDataField *iout
,GwyWindowingType windowing
,GwyTransformDirection direction
,GwyInterpolationType interpolation
,gboolean preserverms
,gint level
);
Calculates 2D Fast Fourier Transform of a rectangular a data field.
If requested a windowing and/or leveling is applied to preprocess data to obtain reasonable results.
Lateral dimensions, offsets and units are unchanged. See
gwy_data_field_fft_postprocess()
for that.
rin |
Real input data field. |
|
iin |
Imaginary input data field. It can be |
|
rout |
Real output data field, it will be resized to area size. |
|
iout |
Imaginary output data field, it will be resized to area size. |
|
windowing |
Windowing type. |
|
direction |
FFT direction. |
|
interpolation |
Interpolation type. |
|
preserverms |
|
|
level |
0 to perform no leveling, 1 to subtract mean value, 2 to subtract plane (the number can be interpreted as the first polynomial degree to keep, but only the enumerated three values are available). |
void gwy_data_field_area_2dfft (GwyDataField *rin
,GwyDataField *iin
,GwyDataField *rout
,GwyDataField *iout
,gint col
,gint row
,gint width
,gint height
,GwyWindowingType windowing
,GwyTransformDirection direction
,GwyInterpolationType interpolation
,gboolean preserverms
,gint level
);
Calculates 2D Fast Fourier Transform of a rectangular area of a data field.
If requested a windowing and/or leveling is applied to preprocess data to obtain reasonable results.
rin |
Real input data field. |
|
iin |
Imaginary input data field. It can be |
|
rout |
Real output data field, it will be resized to area size. |
|
iout |
Imaginary output data field, it will be resized to area size. |
|
col |
Upper-left column coordinate. |
|
row |
Upper-left row coordinate. |
|
width |
Area width (number of columns), must be at least 2. |
|
height |
Area height (number of rows), must be at least 2. |
|
windowing |
Windowing type. |
|
direction |
FFT direction. |
|
interpolation |
Interpolation type. Ignored since 2.8 as no resampling is performed. |
|
preserverms |
|
|
level |
0 to perform no leveling, 1 to subtract mean value, 2 to subtract plane (the number can be interpreted as the first polynomial degree to keep, but only the enumerated three values are available). |
void gwy_data_field_2dfft_raw (GwyDataField *rin
,GwyDataField *iin
,GwyDataField *rout
,GwyDataField *iout
,GwyTransformDirection direction
);
Calculates 2D Fast Fourier Transform of a data field.
No leveling, windowing nor scaling is performed.
The normalisation of FFT is symmetrical, so transformations in both directions are unitary.
Since 2.8 the dimensions need not to be from the set of sizes returned
by gwy_fft_find_nice_size()
.
Lateral dimensions, offsets and units are unchanged. See
gwy_data_field_fft_postprocess()
for that.
Since 2.53 iout
can be NULL
for complex-to-real transforms. Note that
this means Hermitean symmetry of the input data is assumed, i.e. about half
of the input is ignored. If you want to extract the real part of a complex
transform, you must pass a non-NULL
iout
.
rin |
Real input data field. |
|
iin |
Imaginary input data field. It can be |
|
rout |
Real output data field, it will be resized to |
|
iout |
Imaginary output data field, it will be resized to |
|
direction |
FFT direction. It should be |
Since: 2.1
void
gwy_data_field_2dfft_humanize (GwyDataField *data_field
);
Rearranges 2D FFT output to a human-friendly form.
Top-left, top-right, bottom-left and bottom-right sub-rectangles are swapped to obtain a humanized 2D FFT output with (0,0) in the centre.
More precisely, for even field dimensions the equally-sized blocks starting with the Nyquist frequency and with the zero frequency (constant component) will exchange places. For odd field dimensions, the block containing the zero frequency is one item larger and the constant component will actually end up in the exact centre.
Also note if both dimensions are even, this function is involutory and
identical to gwy_data_field_2dfft_dehumanize()
. However, if any dimension
is odd, gwy_data_field_2dfft_humanize()
and
gwy_data_field_2dfft_dehumanize()
are different, therefore they must be
paired properly.
data_field |
A data field. |
void
gwy_data_field_2dfft_dehumanize (GwyDataField *data_field
);
Rearranges 2D FFT output back from the human-friendly form.
Top-left, top-right, bottom-left and bottom-right sub-rectangles are swapped to reshuffle a humanized 2D FFT output back into the natural positions.
See gwy_data_field_2dfft_humanize()
for discussion.
data_field |
A data field. |
Since: 2.8
void gwy_data_field_fft_postprocess (GwyDataField *data_field
,gboolean humanize
);
Updates units, dimensions and offsets for a 2D FFT-processed field.
The field is expected to have dimensions and units of the original direct-space data. The lateral units and resolutions are updated to correspond to its Fourier transform.
The real dimensions are set for spatial frequencies, not wavevectors.
For wavevector lateral coordinates, mutiply all real dimensions and
offsets by 2*G_PI
.
If humanize
is TRUE
gwy_data_field_2dfft_humanize()
is applied to the
field data and the lateral offsets are set accordingly. Otherwise the
offsets are cleared.
Value units are kept intact.
data_field |
A data field. |
|
humanize |
|
Since: 2.38
void gwy_data_field_fft_filter_1d (GwyDataField *data_field
,GwyDataField *result_field
,GwyDataLine *weights
,GwyOrientation orientation
,GwyInterpolationType interpolation
);
Performs 1D FFT filtering of a data field.
data_field |
A data field to filter. |
|
result_field |
A data field to store the result to. It will be resampled
to |
|
weights |
Filter weights for the lower half of the spectrum (the other half is symmetric). Its size can be arbitrary, it will be interpolated. |
|
orientation |
Filter direction. |
|
interpolation |
The interpolation to use for resampling. |
void gwy_data_field_cwt (GwyDataField *data_field
,GwyInterpolationType interpolation
,gdouble scale
,Gwy2DCWTWaveletType wtype
);
Computes a continuous wavelet transform (CWT) at given scale and using given wavelet.
data_field |
A data field. |
|
interpolation |
Interpolation type. Ignored since 2.8 as no resampling is performed. |
|
scale |
Wavelet scale. |
|
wtype |
Wavelet type. |