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DOC: Add a notebook on PSD estimation methods #925

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6f6191f
Add a notebook on PSD estimation methods
GregoryAshton Mar 12, 2025
c1172cb
Switch backend for the new tutorial
GregoryAshton Mar 12, 2025
e056c38
Add installation of memspectrum
GregoryAshton Mar 12, 2025
6e6c4ef
Clean up the notebook ready for discussion
GregoryAshton Mar 25, 2025
7bed4f0
Fix typo
GregoryAshton Mar 25, 2025
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13 changes: 6 additions & 7 deletions bilby/gw/detector/interferometer.py
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Original file line number Diff line number Diff line change
Expand Up @@ -639,16 +639,15 @@ def matched_filter_snr(self, signal):
def whiten_frequency_series(self, frequency_series : np.array) -> np.array:
"""Whitens a frequency series with the noise properties of the detector

.. math::
\\tilde{a}_w(f) = \\tilde{a}(f) \\sqrt{\\frac{4}{T S_n(f)}}

Such that
Given a frequency series :math:`\\tilde{a}_w(f)`, whiten the data by applying

.. math::
Var(n) = \\frac{1}{N} \\sum_{k=0}^N n_W(f_k)n_W^*(f_k) = 2
\\tilde{a}_w(f) = \\tilde{a}(f) \\sqrt{\\frac{4}{T S_n(f)}}\\,,`

Where the factor of two is due to the independent real and imaginary
components.
where :math:`S_n(f)` is the Power Spectral Density (PSD). If the PSD correctly
describes the properties of the data, the resulting whitened frequency series
will be whitened in the sense that the real and imaginary components will be
standard normal random variables.

Parameters
==========
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3 changes: 2 additions & 1 deletion docs/index.txt
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Expand Up @@ -35,12 +35,13 @@ Welcome to bilby's documentation!

.. toctree::
:maxdepth: 1
:caption: Examples:
:caption: Tutorials:

making_priors
compare_samplers
fitting_with_x_and_y_errors
visualising_the_results
power_spectral_density_estimation

.. currentmodule:: bilby

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