From 867533033af56b95598551bfa6b0b596d32a8b82 Mon Sep 17 00:00:00 2001 From: Anders Wallin Date: Sun, 3 Dec 2023 19:19:35 +0200 Subject: [PATCH] docs --- allantools/allantools.py | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/allantools/allantools.py b/allantools/allantools.py index 2d0b9b1..c9714f9 100644 --- a/allantools/allantools.py +++ b/allantools/allantools.py @@ -181,8 +181,8 @@ def mdev(data, rate=1.0, data_type="phase", taus=None): .. math:: \\sigma^2_{MDEV}(m\\tau_0) = { 1 \\over 2 (m \\tau_0 )^2 (N-3m+1) } - \\sum_{j=1}^{N-3m+1} \\lbrace - \\sum_{i=j}^{j+m-1} {x}_{i+2m} - 2x_{i+m} + x_{i} \\rbrace^2 + \\sum_{j=1}^{N-3m+1} \\left[ + \\sum_{i=j}^{j+m-1} {x}_{i+2m} - 2x_{i+m} + x_{i} \\right]^2 Parameters ---------- @@ -843,14 +843,13 @@ def totdev(data, rate=1.0, data_type="phase", taus=None): Where :math:`x^*_i` is a new time-series of length :math:`3N-4` derived from the original phase time-series :math:`x_n` of length :math:`N` by reflection at both ends. + The original data :math:`x_n` is in the center of :math:`x^*`: + + .. math:: - FIXME: better description of reflection operation. - the original data x is in the center of x*: - x*(1-j) = 2x(1) - x(1+j) for j=1..N-2 - x*(i) = x(i) for i=1..N - x*(N+j) = 2x(N) - x(N-j) for j=1..N-2 - x* has length 3N-4 - tau = m*tau0 + x^*_{1-j} = 2x_1 - x_{1+j} for j=1..N-2 + x^*_i = x_i for i=1..N + x^*_{N+j} = 2x_N - x_{N-j} for j=1..N-2 FIXME: bias correction http://www.wriley.com/CI2.pdf page 5