Follow-up to #167 — fixes a numerical issue in the merged implementation, addresses the review comment on readthedocs/sphinx math formatting, and adds a worked multi-clock example. - #169
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…ingle-segment f_nodes The kernel integral J(mu) = int q(z) sin^4(z)/z^(3+mu) dz has a slowly decaying oscillatory tail that naive quad() silently truncates as mu -> -2: the returned value plateaus near 3.3 while the true integral diverges as 3/(8(2+mu)), so the fitted PSD intensity h was wrong by up to ~100x at mu = -1.99 with no warning (and the ADEV round trip still closed, since both directions evaluate the same truncated integral). The tail is now evaluated analytically: the divergent constant term of the cosine expansion of q(z) sin^4(z) in closed form, the bounded oscillatory terms via cosine-weighted QAWF quadrature. Single-slope inputs now recover their analytic coefficients (white FM h0 = 2A^2, flicker FM h = sigma^2/(2 ln 2)) to machine precision; mid-range results are unchanged. Also: - convergence guards are now strict (-2 < mu < 2 ADEV, -2 < mu < 4 HDEV; the boundaries themselves are divergent) and the error messages say what to do instead (MDEV for tau^-1 white/flicker-PM regions, drift removal or vartype='hdev' for tau-linear drift); - psd_piecewise_to_adev() and noise.timmer_koenig_from_psd() accept the two-endpoint f_nodes form that adev2psd_piecewise_approx() returns for single-segment inputs; - docstrings reworked with readthedocs/sphinx-compatible math (follow-up to the review comment on aewallin#167); docs build verified clean; - regression tests, including the single-slope analytic checks that a round trip alone cannot provide. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Replaces the single-clock demo with a worked example (OCXO, AccuBeat USO, Orolia RAFS): ADEV spec -> piecewise PSD -> exact round trip -> Timmer-Koenig noise -> OADEV of the realisations, all overlaid in one figure. The timestep (Nyquist above the highest PSD node) and duration (f1 = 1/T below the lowest node, tau <~ T/10 usable) choices are explained in the module docstring. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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coverage: 89.064% (+3.0%) from 86.055% — kimonito98:fix/adev2psd-analytic-tail-docs into aewallin:master |
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