Design Step

$
\begin{aligned}
\textbf{Given:} \\
\text{At passband:} &\quad \alpha_p = \alpha_{\text{max}} \\
\text{At stopband:} &\quad \alpha_s = \alpha_{\text{min}} \\
\end{aligned}
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\textbf{Order of the Chebyshev Filter:}
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$
n = \frac{ \cosh^{-1} \left( \sqrt{ \frac{10^{\frac{\alpha_{\text{min}}}{10}} - 1}{10^{\frac{\alpha_{\text{max}}}{10}} - 1} } \right) }{ \cosh^{-1} \left( \frac{\omega_s}{\omega_p} \right) }
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\textbf{Ripple Factor:}
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\varepsilon = \sqrt{10^{\frac{\alpha_{\text{max}}}{10}} - 1}
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\textbf{Component Definitions for } u_k \text{ and } v:
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u_k = \frac{(2k + 1)\pi}{2n}, \quad \text{for } k = 0, 1, 2, \ldots, 2n+1
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v = \pm \frac{1}{n} \sinh^{-1} \left( \frac{1}{\varepsilon} \right)
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\textbf{Compute Hyperbolic Trig Values:}
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\sinh(v), \quad \cosh(v)
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\textbf{Chebyshev Poles:}
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$
\begin{aligned}
\sigma_k &= -\sin\left( \frac{(2k + 1)\pi}{2n} \right) \sinh(v) \\
\omega_k &= \cos\left( \frac{(2k + 1)\pi}{2n} \right) \cosh(v) \\
S_k &= \sigma_k \pm j \omega_k
\end{aligned}
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\textbf{Pole Frequency and Q-Factor:}
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W_k = \sqrt{ \sigma_k^2 + \omega_k^2 }
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Q_k = \frac{W_k}{2|\sigma_k|}
$