highpass_fft_filter#

kikuchipy.filters.highpass_fft_filter(shape: tuple[int, int], cutoff: int | float, cutoff_width: int | float | None = None) → ndarray[source]#

Return a frequency domain high-pass filter transfer function in 2D.

Used in [Wilkinson et al., 2006].

Parameters:

shape: Shape of function.
cutoff: Cut-off frequency.
cutoff_width: Width of cut-off region. If not given (default), it is set to half of the cutoff frequency.

Returns:

window: 2D transfer function.

Notes

The high-pass filter transfer function is defined as

\[\begin{split}w(r) = e^{-\left((c - r)/(\sqrt{2}w_c/2)\right)^2}, w(r) = \begin{cases} 0, & r < c - 2w_c\\ 1, & r > c, \end{cases}\end{split}\]

where \(r\) is the radial distance to the window centre, \(c\) is the cut-off frequency, and \(w_c\) is the width of the cut-off region.

Examples

>>> import numpy as np
>>> import kikuchipy as kp
>>> w1 = kp.filters.Window(
...     "highpass", cutoff=1, cutoff_width=0.5, shape=(96, 96)
... )
>>> w2 = kp.filters.highpass_fft_filter(
...     shape=(96, 96), cutoff=1, cutoff_width=0.5
... )
>>> np.allclose(w1, w2)
True

highpass_fft_filter#

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