Final answer:
To plot the pole-zero diagram of H(s)H(−s), we need to find the roots of the magnitude-squared equation for the frequency response. The pole-zero diagram consists of poles at Ω = ±5, ±i5, ±i125.
Step-by-step explanation:
To plot the pole-zero diagram of H(s)H(−s), we need to find the roots of the magnitude-squared equation for the frequency response. First, let's rewrite the equation as a polynomial equation by multiplying both sides by the denominator (Ω⁶ + 151Ω⁴ + 15772Ω² + 15625) and moving the terms to one side.
Ω⁶ + 151Ω⁴ + 15772Ω² + 15625 - 656Ω⁶/(Ω⁶ + 151Ω⁴ + 15772Ω² + 15625) = 0
Simplifying further, we get:
(Ω² - 25)(Ω² + 25)(Ω² + 125) = 0
From this equation, we can see that the roots, or poles, of the equation are Ω = ±5, ±i5, ±i125. The zeros of the equation, which are the roots of H(−s), are the same as the poles. Therefore, the pole-zero diagram of H(s)H(−s) consists of poles at Ω = ±5, ±i5, ±i125.