1. The transfer function $H_6(s)$ represents a sixth-order prototype Butterworth filter.
(a) Give $H_6(s)$ in quadratic factored form (The usual form). The coefficients should contain trigonometric functions using the symbol $\pi$, but not the symbol $k$. Don't use a calculator.
(b) What is the gain $|H_6(j\Omega)|$ at $\Omega = 1$ rad/sec.? Don't use db.
(c) The kth denominator factor of the Butterworth filter $H_n(s)$, before multiplying it out, is $(s - e^{j\theta(k)}) (s - e^{-j\theta(k)})$. Remembering that the real part of a Butterworth pole $e^{j\theta(k)}$ is multiplied by $\beta$ to produce a Chebyshev pole, write the kth Chebyshev second order denominator using trigonometric functions, the symbol $\theta(k)$, and the symbol $\beta$.
