Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

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7 \draw[fill=black] (1.28934,1.53934) circle (0.08);
8 \draw[fill=black] (3.41066,1.53934) circle (0.08);
9 \node[] at (2.35000,5.00000) {$\eta^4=-1$};
10 \node[] at (2.35000,0.05000) {exponent plane};
11 \draw[black!13] (5.20000,1.00000) -- (5.20000,4.00000);
12 \node[font=\sffamily\footnotesize] at (5.20000,0.69000) {$0$};
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14 \node[font=\sffamily\footnotesize] at (7.02500,0.69000) {$\pi/2$};
15 \draw[black!13] (8.85000,1.00000) -- (8.85000,4.00000);
16 \node[font=\sffamily\footnotesize] at (8.85000,0.69000) {$\pi$};
17 \draw[black!13] (10.67500,1.00000) -- (10.67500,4.00000);
18 \node[font=\sffamily\footnotesize] at (10.67500,0.69000) {$3\pi/2$};
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20 \node[font=\sffamily\footnotesize] at (12.50000,0.69000) {$2\pi$};
21 \draw[black!13] (5.20000,1.42830) -- (12.50000,1.42830);
22 \node[anchor=east,font=\sffamily\footnotesize] at (5.04000,1.42830) {$1/\sqrt2$};
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28 \node[] at (8.90000,4.65000) {$h_4(\theta)=\frac{|\cos\theta|+|\sin\theta|}{\sqrt2}$};
29 \node[] at (8.90000,0.05000) {minima: two dominant exponentials tie};
30 \end{tikzpicture}

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