Gwyddion – Free SPM (AFM, SNOM/NSOM, STM, MFM, …) data analysis software

inttrans (HEAD)

inttrans — FFT and other integral transforms

Functions

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 ()

Includes

#include <libprocess/gwyprocess.h>

Description

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

FFTW3

routines.

Functions

gwy_fft_find_nice_size ()

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.

Parameters

size

Transform size.

 

Returns

A nice FFT array size.

gwy_data_line_fft ()

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.

Parameters

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

TRUE to preserve RMS value while windowing.

 

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).

 

gwy_data_line_part_fft ()

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.

Parameters

rsrc

Real input data line.

 

isrc

Imaginary input data line. Since 2.7 it can be NULL for real-to-complex transforms.

 

rdest

Real output data line, it will be resized to len .

 

idest

Imaginary output data line, it will be resized to len .

 

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

TRUE to preserve RMS value while windowing.

 

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).

 

gwy_data_line_fft_raw ()

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().

Parameters

rsrc

Real input data line.

 

isrc

Imaginary input data line. Since 2.7 it can be NULL for real-to-complex transform.

 

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

gwy_data_field_1dfft ()

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.

Parameters

rin

Real input data field.

 

iin

Imaginary input data field. It can be NULL for real-to-complex transform which can be somewhat faster than complex-to-complex transform.

 

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 GWY_ORIENTATION_HORIZONTAL to transform rows, GWY_ORIENTATION_VERTICAL to transform columns.

 

windowing

Windowing type.

 

direction

FFT direction.

 

interpolation

Interpolation type. Ignored since 2.8 as no resampling is performed.

 

preserverms

TRUE to preserve RMS while windowing.

 

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).

 

gwy_data_field_area_1dfft ()

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.

Parameters

rin

Real input data field.

 

iin

Imaginary input data field. It can be NULL for real-to-complex transform which can be somewhat faster than complex-to-complex transform.

 

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 GWY_ORIENTATION_HORIZONTAL to transform rows, GWY_ORIENTATION_VERTICAL to transform columns.

 

windowing

Windowing type.

 

direction

FFT direction.

 

interpolation

Interpolation type. Ignored since 2.8 as no resampling is performed.

 

preserverms

TRUE to preserve RMS while windowing.

 

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).

 

gwy_data_field_1dfft_raw ()

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().

Parameters

rin

Real input data field.

 

iin

Imaginary input data field. It can be NULL for real-to-complex transform.

 

rout

Real output data field, it will be resized to rin size.

 

iout

Imaginary output data field, it will be resized to rin size.

 

orientation

Orientation: pass GWY_ORIENTATION_HORIZONTAL to transform rows, GWY_ORIENTATION_VERTICAL to transform columns.

 

direction

FFT direction.

 

Since: 2.1

gwy_data_field_2dfft ()

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.

Parameters

rin

Real input data field.

 

iin

Imaginary input data field. It can be NULL for real-to-complex transform which can be somewhat faster than complex-to-complex transform.

 

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

TRUE to preserve RMS while windowing.

 

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).

 

gwy_data_field_area_2dfft ()

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.

Parameters

rin

Real input data field.

 

iin

Imaginary input data field. It can be NULL for real-to-complex transform which can be somewhat faster than complex-to-complex transform.

 

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

TRUE to preserve RMS while windowing.

 

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).

 

gwy_data_field_2dfft_raw ()

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 .

Parameters

rin

Real input data field.

 

iin

Imaginary input data field. It can be NULL for real-to-complex transform.

 

rout

Real output data field, it will be resized to rin size.

 

iout

Imaginary output data field, it will be resized to rin size.

 

direction

FFT direction. It should be GWY_TRANSFORM_DIRECTION_FORWARD for real-to-complex transforms and GWY_TRANSFORM_DIRECTION_BACKWARD for complex-to-real transforms.

 

Since: 2.1

gwy_data_field_2dfft_humanize ()

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.

Parameters

data_field

A data field.

 

gwy_data_field_2dfft_dehumanize ()

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.

Parameters

data_field

A data field.

 

Since: 2.8

gwy_data_field_fft_postprocess ()

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.

Parameters

data_field

A data field.

 

humanize

TRUE to rearrange data to have the frequency origin in the centre.

 

Since: 2.38

gwy_data_field_fft_filter_1d ()

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.

Parameters

data_field

A data field to filter.

 

result_field

A data field to store the result to. It will be resampled to data_field 's size.

 

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.

 

gwy_data_field_cwt ()

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.

Parameters

data_field

A data field.

 

interpolation

Interpolation type. Ignored since 2.8 as no resampling is performed.

 

scale

Wavelet scale.

 

wtype

Wavelet type.

 
© David Nečas and Petr Klapetek

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