Editing Rayleigh fading (section)

===Butterworth filter as Doppler power spectral density===

[[File:Rayleigh fading.png|thumb|320px|Filtered by Butterworth filter Rayleigh time series (Sampling frequency is 120 Hz.)]]

According to <ref>Fernando Pérez-Fontán, Iria Sanchez-Lago, Roberto Prieto Cerdeira, andAna Bolea-Alama nac. Consolidation of a multi-state narrowband land mo-bile satellite channel model. In The Second European Conference on Anten-nas and Propagation, EuCAP 2007., pages 1 –6, nov. 2007</ref><ref>Fontæn, F.P. and Espiæeira, P.M., 2008. [https://d1wqtxts1xzle7.cloudfront.net/60491689/Modelling.the.Wireless.Propagation.Channel20190904-14283-1j7pfux-with-cover-page-v2.pdf?Expires=1634677755&Signature=R~6XK97YX7dUMo8uXdvNePiL4XPYpUVAPmzv5UoMotLHtuFPsAS776PgSP80s-aNs1CKZXN95YCwgz5CNf5GMLTJTRqp1YAYKnEX0urYDqO~w62jiFR-ruKNjUJoYUvB~I2uUXPty3Swa7P19axRmxvf2ZWpMZe83ewMCQ3PmC6UbtTpdSUyGNFGl-RHgAPDCFosfgLcyVqZz8RJTrmClZpj8huspz3YBmlnTmgYcD7wOqFu2trDG4qAy5mEU-uXGbiOpD98qYF7suR3h43Ld3Ft3toGon7ENOaHrz0NLTJ9c-9SQHqbBV1yuI5qiWXqQktFdj-GS0Swpo7trBBIXg__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA Modelling the wireless propagation channel: a simulation approach with Matlab] (Vol. 5). John Wiley & Sons. -  p. 123 - 129</ref><ref>[https://www.db-thueringen.de/rsc/viewer/dbt_derivate_00032343/ilm1-2015000358.pdf?page=40 Arndt, D., 2015. On channel modelling for land mobile satellite reception] (Doctoral dissertation). - p. 28</ref> Doppler [[Spectral density|PSD]] can also be modeled via [[Butterworth filter]] as:

:<math>S_{Doppler}(f) = |H_{Butterworth}|^2 = \frac{B}{\sqrt{1 - (f/f_0)^{2k}}}</math>

where ''f'' is a frequency, <math>H_{Butterworth}</math> is the Butterworth filter response, ''B'' is the normalization constant, ''k'' is the filter order and <math>f_0</math> is the [[Cutoff frequency]] which should be selected with respect to maximum Doppler shift.