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Andrey Akinshin edited Prony 2D.tex
almost 9 years ago
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\section{Prony \section{Trigonometric real Prony, 2D}
$$
m_k = a_1 e^{-2\pi i \mu_1 k \delta} + a_2 e^{-2\pi i \mu_2 k \delta}.
$$
On the following figure, you can see equipotential surfaces of the field
$$
F(a_1, a_2, d\mu) = \sqrt{\Delta m_0^2 + \Delta m_1^2 + \Delta m_2^2 + \Delta m_3^2}, \quad \Delta m_k = m_{A,k} - m_{B,k}
$$
where
$$
\begin{array}{l}
S_A \in (a = \{1, 1\}, \mu = \{-0.04, 0.04\}) \; \ldots \; (a = \{1, 1\}, \mu = \{-2.5, 2.5\}) \\
S_B(a_1, a_2, d\mu) = (a = \{a_1, a_2\}, \mu = \{ -d\mu/2, d\mu/2 \})
\end{array}
$$