.. _book_fig_chapter10_fig_FFT_aliasing:


The effect of Sampling
----------------------
Figure 10.3

A visualization of aliasing in the Fourier transform. In each set of four
panels, the top-left panel shows a signal and a regular sampling function, the
top-right panel shows the Fourier transform of the signal and sampling
function, the bottom-left panel shows the sampled data, and the bottom-right
panel shows the convolution of the Fourier-space representations (cf. figure
10.2). In the top four panels, the data is well sampled, and there is little
to no aliasing. In the bottom panels, the data is not well sampled (the spacing
between two data points is larger) which leads to aliasing, as seen in the
overlap of the convolved Fourier transforms (figure adapted from Greg05).



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.. image:: ../images/chapter10/fig_FFT_aliasing_1.png
    :align: center
    :scale: 100



.. image:: ../images/chapter10/fig_FFT_aliasing_2.png
    :align: center
    :scale: 100



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