Fourier transform

In order to interpret EXAFS spectra, it is useful to analyze the fourier-transform of the data. The fourier command calculates the transform, adding the calculated result to the fourier domain of the file.

The command requires the input and output ranges of the data. The input range is taken from the real domain, and can be expressed in eV or k, while the output range is in the fourier domain, thus can only be expressed in Angstrom. While the input range is expressed as (start) (end), the output Fourier range is expressed as (end) (spacing), as the beginning of the Fourier range is by default set to 0.

The command adds a win column, containing the window function, to the real domain, and creates the fourier domain containing the R index column and the f complex valued column.

fourier <range> <output> [--options]

Argument	Explanation
<range>	The range considered to perform the fourier transform. See Number and unit specification for the range syntax explanation.
--kweight / -k <value>	Performs the operation on data weighed by the specified factor: \(k^{n}\cdot\chi(k)\). By default, does not weigh the data (equal to a kweight of 0).
--apodizer / -a <apodizer>	The apodizing window shape. By default, uses a Hann window. The available windows are listed in the related section
--width / -w <value>	The width of the ramps of the window. See the related section for a visual explanation of this parameter.
--method <method>	<div><p>Uses a different method to perform the fourier transform.</p><ul><li>dft is the default method, and uses matrix multiplication to calculate the transform</li><li>finuft uses the finufft.nufft1d3 method</li><li>fft uses the numpy rfft method, which requires the data to be uniformly spaced.</li></ul></div>

Apodizer

Each apodizing window is defined by its first three letters. Some apodizers require an additional parameter, such as the exponential window and the gaussian window. This parameter is included in the window definition, separated by :.

Window	Description
han	Hann window
sin	Sine window
rec	Rectangular window
bar	Bartlett window, also called triangular window.
wel	Welch window
exp:p	Exponential window. The parameter modifies the window as \(\exp(- p\cdot t)\)
gau:p	Gaussian window. The parameter modifies the window as \(\exp(-p \cdot x^2)\)

Example

fourier 3k 12k 6A 0.01A -a hann -k2 -w1

This snippet calculates the fourier transform of the \(k^2\)-weighed data between 3k and 12k, from 0A to 6A with a spacing of 0.01A using a hann window of width 1k.

Phase manipulation

To perform manipulations on the phase of the fourier-transform data, the phase command can be used. This command does not modify the intensity of the fourier data, but only its phase.

Phase alignment

phase align

This command aligns all the spectra to minimize the distance to the first spectrum. The result is that, in the complex space, all spectra get rotate to align themselves to the first spectrum.

Phase correction

phase correct

This command estimates a linear contribution from each spectrum, and corrects it. The removed contribution is set to the column pcorr. This operation is analoguous to NMR phase correction.