XASFT module

The xasft module offers the following functions to perform discrete fast Fourier transforms (FFT) on a XAFS scan:

Function

Description

ftwindow()

Returns a FT window.

xftf()

Calculates a forward FFT of a XAFS signal.

xftr()

Calculates a reverse FFT of a XAFS signal.

xftf_kwin()

Calculates a forward FFT of a preset XAFS signal.

xftr_kwin()

Calculates a reverse FFT of a preset XAFS signal.
araucaria.xas.xasft.ftwindow(x, x_range=[- inf, inf], dx1=1, dx2=None, win='hanning')[source]

Returns a FT window.

Parameters

  • x (ndarray) – Array for the FT window.

  • x_range (list) – Range for the FT window. The default is [-inf, inf].

  • dx1 (float) – First tapering parameter for FT window. The defaut is 1.

  • dx2 (Optional[float]) – Second tapering parameter for FT window. If None it will use the same value as dx1.

  • win (str) – Name of the window type. The default is ‘hanning’. See Notes for valid names.

Return type

ndarray

Returns

1-d array with the FT window.

Raises

ValueError – If window name is not recognized.

Notes

Valid window names:

  • ‘hanning’ : cosine-squared function window.

  • ‘parzen’ : linear function window.

  • ‘welch’ : quadratic function window.

  • ‘gaussian’ : Gaussian (normal) function window.

  • ‘sine’ : sine function window.

  • ‘kaiser’ : Kaiser-Bessel function-derived window.

Example

>>> from numpy import arange
>>> import matplotlib.pyplot as plt
>>> from araucaria.xas import ftwindow
>>> from araucaria.plot import fig_xas_template
>>> k       = arange(0, 10.1, 0.05)
>>> k_range = [2,8]
>>> windows = ['hanning', 'parzen', 'welch',
...            'gaussian', 'sine', 'kaiser']
>>> dk      = 1.0
>>> fig_kws = {'sharex' : True}
>>> fig, axes = fig_xas_template(panels='ee/ee/ee', **fig_kws)
>>> for i, ax in enumerate(axes.flatten()):
...     win  = ftwindow(k, k_range, dk, win= windows[i])
...     line = ax.plot(k, win, label=windows[i])
...     for val in k_range:
...         line = ax.axvline(val - dk/2, color='gray', ls=':')
...         line = ax.axvline(val + dk/2, color='gray', ls=':')
...     leg  = ax.legend()
...     text = ax.set_ylabel('')
...     text = ax.set_xlabel('')
>>> fig.tight_layout()
>>> plt.show(block=False)

(Source code, png, hires.png, pdf)

../_images/xas_ft-1.png
araucaria.xas.xasft.xftf(group, k_range=[0, 20], kweight=0, dk1=1, dk2=None, win='hanning', rmax_out=10, nfft=2048, kstep=0.05, with_phase=False, update=False)[source]

Calculates a forward FFT of a XAFS signal.

A XAFS forward FFT decomposes \(\chi(k)\) into \(\chi(R)\).

Parameters

  • group (Group) – Group containing chi(k) for the forward FT.

  • k_range (list) – Photoelectron wavenumber range for the FT (\(Å^{-1}\)). The default is [0, 20].

  • kweight (int) – Exponent for weighting chi(k) by k**kweight. The default is 0.

  • dk1 (float) – First tapering parameter for the FT window. The detault is 1.

  • dk2 (Optional[float]) – Second tapering parameter for FT window. If None it will take the value of dk1.

  • win (str) – Name of the FT window type. The default is ‘hanning’.

  • rmax_out (float) – Highest R value for \(\chi(R)\) (Å). The default is 10.

  • nfft (int) – Array size for the FT. The default is 2048.

  • kstep (float) – Wavenumber step size for the FT (\(Å^{-1}\)). The default is 0.05.

  • with_phase (bool) – Return the phase as well as magnitude, real, and imaginary parts. The default is False.

  • update (bool) – Indicates if the group should be updated with the ftkf attributes. The default is False.

Return type

dict

Returns

Dictionary with the following arguments:

  • kwin : array with the FT window.

  • r : array with R values (Å).

  • chir : array with \(\chi(R)\).

  • chir_mag : array with magnitude of \(\chi(R)\).

  • chir_re : array with real part of \(\chi(R)\).

  • chir_im : array with imaginary part of \(\chi(R)\).

  • chir_pha : array with phase of \(\chi(R)\). Returned if with_phase=True.

Raises

  • TypeError – If group is not a valid Group instance.

  • AttributeError – If attribute k or chi does not exist in group.

Notes

If update=True the contents of the returned dictionary will be included as attributes of group.

Example

>>> from araucaria.testdata import get_testpath
>>> from araucaria import Group
>>> from araucaria.io import read_dnd
>>> from araucaria.xas import pre_edge, autobk, xftf
>>> from araucaria.utils import check_objattrs
>>> kw      = 2
>>> k_range = [2,10]
>>> fpath   = get_testpath('dnd_testfile1.dat')
>>> group   = read_dnd(fpath, scan='mu')  # extracting mu and mu_ref scans
>>> pre     = pre_edge(group, update=True)
>>> autbk   = autobk(group, update=True)
>>> fft     = xftf(group, k_range=k_range, kweight=kw, update=True)
>>> attrs = ['kwin', 'r', 'chir', 'chir_mag', 'chir_re', 'chir_im']
>>> check_objattrs(group, Group, attrs)
[True, True, True, True, True, True]

>>> # plotting forward FFT signal
>>> import matplotlib.pyplot as plt
>>> from araucaria.plot import fig_xas_template
>>> fig, ax = fig_xas_template(panels='er', fig_pars={'kweight':kw})
>>> line = ax[0].plot(group.k, group.k**kw*group.chi)
>>> line = ax[0].plot(group.k, group.kwin, color='firebrick')
>>> xlim = ax[0].set_xlim(0,12)
>>> line = ax[1].plot(group.r, group.chir_mag)
>>> xlim = ax[1].set_xlim(0,6)
>>> fig.tight_layout()
>>> plt.show(block=False)

(Source code, png, hires.png, pdf)

../_images/xas_ft-2.png
araucaria.xas.xasft.xftr(group, r_range=[0, 20], rweight=0, dr1=1, dr2=None, win='hanning', nfft=2048, kstep=0.05, qmax_out=20, with_phase=False, update=False)[source]

Calculates a reverse FFT of a XAFS signal.

A XAFS reverse FFT recovers \(\chi(q)\) from \(\chi(R)\).

Parameters

  • group (Group) – Group containing chi(k) for the forward FT.

  • r_range (list) – R range for the reverse FT (Å). The default is [0, 20].

  • rweight (int) – Exponent for weighting chi(R) by R**rweight. The default is 0.

  • dr1 (float) – First tapering parameter for the reverse FT window. The default is 1.

  • dr2 (Optional[float]) – Second tapering parameter for reverse FT window. If None it will take the value of dr1.

  • win – Name of the FT window type. The default is ‘hanning’.

  • qmax_out (float) – Highest q value for \(\chi(R)\) ((\(Å^{-1}\))). The default is 20.

  • nfft (int) – Array size for the reverse FT. The default is 2048.

  • kstep (float) – Wavenumber step size for the reverse FT (\(Å^{-1}\)). The default is 0.05.

  • with_phase (bool) – Return the phase as well as magnitude, real, and imaginary parts. The default is False.

  • update (bool) – Indicates if the group should be updated with the ftkf attributes. The default is False.

Return type

dict

Returns

Dictionary with the following arguments:

  • rwin : array with the reverse FT window.

  • q : array with q values (Å).

  • chiq : array with \(\chi(R)\).

  • chiq_mag : array with magnitude of \(\chi(q)\).

  • chiq_re : array with real part of \(\chi(q)\).

  • chiq_im : array with imaginary part of \(\chi(q)\).

  • chiq_pha : array with phase of \(\chi(q)\). Returned if with_phase=True.

Raises

  • TypeError – If group is not a valid Group instance.

  • AttributeError – If attribute q or chir does not exist in group.

Notes

If update=True the contents of the returned dictionary will be included as attributes of group.

Example

>>> from araucaria.testdata import get_testpath
>>> from araucaria import Group
>>> from araucaria.io import read_dnd
>>> from araucaria.xas import pre_edge, autobk, xftf, xftr
>>> from araucaria.utils import check_objattrs
>>> kw      = 2
>>> k_range = [2,10]
>>> r_range = [0.5, 2]
>>> fpath   = get_testpath('dnd_testfile1.dat')
>>> group   = read_dnd(fpath, scan='mu')  # extracting mu and mu_ref scans
>>> pre     = pre_edge(group, update=True)
>>> autbk   = autobk(group, update=True)
>>> fft     = xftf(group, k_range=k_range, kweight=kw, update=True)
>>> rft     = xftr(group, r_range=r_range, update=True)
>>> attrs = ['rwin', 'q', 'chiq', 'chiq_mag', 'chiq_re', 'chiq_im']
>>> check_objattrs(group, Group, attrs)
[True, True, True, True, True, True]

>>> # plotting forward FFT signal
>>> import matplotlib.pyplot as plt
>>> from araucaria.plot import fig_xas_template
>>> fig, ax = fig_xas_template(panels='rq', fig_pars={'kweight': kw})
>>> line = ax[0].plot(group.r, group.chir_mag)
>>> line = ax[0].plot(group.r, group.rwin, color='firebrick')
>>> xlim = ax[0].set_xlim(0,6)
>>> line = ax[1].plot(group.k, group.k**kw*group.chi)
>>> line = ax[1].plot(group.q, group.chiq_re)
>>> xlim = ax[1].set_xlim(0,12)
>>> fig.tight_layout()
>>> plt.show(block=False)

(Source code, png, hires.png, pdf)

../_images/xas_ft-3.png
araucaria.xas.xasft.xftf_kwin(chi, nfft=2048, kstep=0.05)[source]

Calculates a forward FFT of a preset XAFS signal.

Parameters

  • chi (ndarray) – Array of \(\chi(k)\) on a uniform grid. Window and k-weighting are assumed to have been already applied to the signal.

  • nfft (int) – Array size for the FFT. The default is 2048.

  • kstep (float) – Photoelectron wavenumber step size for the FFT (\(Å^{-1}\)). The default is 0.05.

Return type

ndarray

Returns

Complex array of \(\chi(R)\).

Example

>>> from numpy import arange, sin, pi
>>> from scipy.fftpack import fftfreq
>>> from araucaria.xas import ftwindow, xftf_kwin
>>> nfft = 2048  # number of points for FFT
>>> ks   = 0.05  # delta k (angstrom^-1)
>>> f1   = 0.5   # freq1 (angstrom)
>>> f2   = 1.2   # freq2 (angstrom)
>>> k    = arange(0, 10, ks)
>>> win  = ftwindow(k, x_range=(0,10), dx1=0.5, win='sine')
>>> chi  = 0.5*sin(2*pi*k*f1) + 0.1*sin(2*pi*k*f2)
>>> chir = xftf_kwin(win*chi, nfft=nfft, kstep=ks)
>>> freq = fftfreq(nfft, ks)
>>> print(chir.dtype)
complex128

>>> # plotting forward FFT signal
>>> import matplotlib.pyplot as plt
>>> from araucaria.plot import fig_xas_template
>>> fig, ax = fig_xas_template(panels='er', fig_pars={'kweight':0})
>>> line = ax[0].plot(k, win*chi)
>>> line = ax[1].plot(freq[:int(nfft/2)], abs(chir[:int(nfft/2)]))
>>> xlim = ax[1].set_xlim(0,2)
>>> xlab = ax[1].set_xlabel('$R/\pi$ [$\AA$]')
>>> for f in (f1,f2):
...     line = ax[1].axvline(f, color='gray', ls=':')
>>> fig.tight_layout()
>>> plt.show(block=False)

(Source code, png, hires.png, pdf)

../_images/xas_ft-4.png
araucaria.xas.xasft.xftr_kwin(chir, nfft=2048, kstep=0.05)[source]

Calculates a reverse FFT of a preset XAFS signal.

Parameters

  • chir (ndarray) – Array of \(\chi(R)\) on a uniform grid. Window and k-weighting are assumed to have been already applied to the signal.

  • nfft (int) – Array size for the FFT. The default is 2048.

  • kstep (float) – Photoelectron wavenumber step size for the FFT (\(Å^{-1}\)). The default is 0.05.

Return type

ndarray

Returns

Complex array for \(\chi(q)\).

Example

>>> from numpy import arange, sin, pi
>>> from scipy.fftpack import fftfreq
>>> from araucaria.xas import ftwindow, xftf_kwin, xftr_kwin
>>> nfft = 2048  # number of points for FFT
>>> ks   = 0.05  # delta k (angstrom^-1)
>>> f1   = 0.5   # freq1 (angstrom)
>>> k    = arange(0, 10, ks)
>>> wink = ftwindow(k, x_range=(0,10), dx1=0.5, win='sine')
>>> chi  = 0.5*sin(2*pi*k*f1)
>>> chir = xftf_kwin(wink*chi, nfft=nfft, kstep=ks)
>>> freq = fftfreq(nfft, ks)[:nfft//2]
>>> chiq = xftr_kwin(chir, nfft=nfft, kstep=ks)[:len(k)]
>>> print(chiq.dtype)
complex128

>>> # plotting reverse FFT signal
>>> import matplotlib.pyplot as plt
>>> from araucaria.plot import fig_xas_template
>>> fig, ax = fig_xas_template(panels='re', fig_pars={'kweight':0})
>>> line = ax[0].plot(freq, abs(chir))
>>> xlim = ax[0].set_xlim(0,2)
>>> xlab = ax[0].set_xlabel('$R/\pi$ [$\AA$]')
>>> line = ax[1].plot(k, chiq)
>>> text = ax[1].set_xlabel(r'$q(\AA^{-1})$')
>>> text = ax[1].set_ylabel(r'$\chi(q)$')
>>> fig.tight_layout()
>>> plt.show(block=False)

(Source code, png, hires.png, pdf)

../_images/xas_ft-5.png