this is for holding javascript data
jBillou edited Estimating phases from signal.tex
over 9 years ago
Commit id: 1f6d50b0ffb27a073961a9e9d7c60812404834be
deletions | additions
diff --git a/Estimating phases from signal.tex b/Estimating phases from signal.tex
index 16f7a60..cb93f15 100644
--- a/Estimating phases from signal.tex
+++ b/Estimating phases from signal.tex
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Explain how we do this stuff
$\textrm{d}\theta =
\omega_1 \frac{2\pi}{T_1} \textrm{d}t + f_1(\theta) + F_1(\theta,\phi) \textrm{d}t + \sigma_1 \textrm{d} W^1_t $
$\textrm{d}\phi =
\omega_2 \frac{2\pi}{T_2} \textrm{d}t + f_2(\theta) + F_2(\theta,\phi) \textrm{d}t + \sigma_2 \textrm{d} W^2_t $
This is a reference \cite{bieler2014}.
...
\begin{align*}
\textrm{d}\theta_t
= \frac{2\pi}{T}\textrm{d}t &= \frac{2\pi}{T_1}\textrm{d}t +
\sigma\textrm{d}W_t \sigma\textrm{d}W_t\\
\textrm{d}\lambda_t
= -\gamma_lambda (\lambda_t-\mu_\lambda) &= -\gamma_{\lambda} (\lambda_t-\mu_{\lambda}) \textrm{d}t +
\sigma_{\lambda}\textrm{d}W_t \sigma_{\lambda}\textrm{d}W_t\\
\textrm{d}B_t
= &= -\gamma_B (B_t-\mu_B) \textrm{d}t + \sigma_{B}
\textrm{d}W_t
\end{align} \textrm{d}W_t\\
\end{align*}