docs(GaussFIR): explain the sqrt(2) in the Doppler filter width constant - #4
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docs(GaussFIR): explain the sqrt(2) in the Doppler filter width constant#4spinkham wants to merge 1 commit into
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The filter's amplitude response must be the square root of the target Gaussian Doppler power spectrum (PSD of filtered noise = |H|^2), which is what the SQRT2 in the sigma constant implements. The original PathSim technical guide's prose describes the construction without calling this out, and at least one downstream reimplementation dropped the sqrt(2) and realized a ~0.71x-narrow Doppler spread as a result. Comment-only change. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
This was referenced Jul 28, 2026
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Comment-only change: documents why
GaussFIR::initusessigma = Fs*sqrt(2)/(2*pi*F2sig).The fading process must have a Gaussian power spectrum with 2-sigma width
F2sig(Watterson / ITU-R F.1487 convention). Since the PSD of filtered white noise is|H(f)|^2, the filter's amplitude response has to be the square root of that Gaussian — itself Gaussian-shaped but sqrt(2) wider — and that sqrt(2) is exactly what the width constant implements. PathSim gets this right, and the derivation chain is now spelled out aboveinit():sigma_t = Fs*sqrt(2)/(2*pi*F2sig)samples|H(f)|: Gaussian,sigma_f = F2sig/sqrt(2)|H(f)|^2: Gaussian,sigma = F2sig/2(2-sigma =F2sig)Why bother documenting it: the prose in the original PathSim technical guide (§4.1.5, "a Gaussian shaped low pass filter") doesn't call the square root out, and we recently traced a downstream open-source reimplementation that followed the description, dropped the sqrt(2), and has been realizing a ~0.71x-narrow Doppler spread ever since (a 1 Hz "poor" channel fading like ~0.7 Hz). A comment at the constant is the cheapest way to stop that from happening again.
No functional change.
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