.. _book_fig_chapter10_fig_sampling:


The effect of Sampling
----------------------
Figure 10.14

An illustration of the impact of measurement errors on the Lomb-Scargle power
(cf. figure 10.4). The top-left panel shows a simulated data set with 40 points
drawn from the function y(t|P) = sin(t) (i.e., f = 1/(2pi) ~ 0.16) with random
sampling. Heteroscedastic Gaussian noise is added to the observations, with a
width drawn from a uniform distribution with 0.1 < sigma < 0.2 (this error
level is negligible compared to the amplitude of variation). The spectral
window function (PSD of sampling times) is shown in the bottom-left panel.
The PSD (:math:`P_{LS}`) computed for the data set from the top-left panel is
shown in the top-right panel; it is equal to a convolution of the single peak
(shaded in gray) with the window PSD shown in the bottom-left panel (e.g., the
peak at f ~ 0.42 in the top-right panel can be traced to a peak at f ~ 0.26 in
the bottom-left panel). The bottom-right panel shows the PSD for a data set
with errors increased by a factor of 10. Note that the peak f ~ 0.16 is now
much shorter, in agreement with eq. 10.47. In addition, errors now exceed the
amplitude of variation and the data PSD is no longer a simple convolution of
a single peak and the spectral window.



.. image:: ../images/chapter10/fig_sampling_1.png
    :scale: 100
    :align: center


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