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Figure 1
Schematic representation of gap effects. The top row shows a continuous function f(x) being filtered by a sampling function [\Phi(x)], introducing a gap of two different sizes. All points outside the gap are sensed [[\Phi(x) = 1]], while those inside the gap are not [[\Phi(x) = 0]]. The middle row shows the Fourier transform of the continuous function F[ f(x)](k) and the Fourier transform of the sampling function [F[\Phi(x)](k)], separately. The larger the gap in the x domain (top row, dashed line), the steeper the resulting Fourier transform becomes in the k domain (middle row, dashed line). This causes the convolution results in the bottom row to deviate more strongly from the Fourier transform of the original function f(x) (middle row, solid line).

Journal logoJOURNAL OF
APPLIED
CRYSTALLOGRAPHY
ISSN: 1600-5767
Volume 58| Part 6| December 2025| Pages 2090-2104
https://doi.org/10.1107/S1600576725010003
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