Consider the output of an envelope detector defined by Equation (2.92), which is reproduced here for convenience y (t) = {[Ac + A_c k_a m (t) + n _l (t)] ² + n²_Q (t)} ^1/2 

(a) Assume that the probability of the event | nQ (t) | > ε A_c | 1 + k_a m (t) | is equal to or less than δ₁, where ε << 1. What is the probability that the effect of the quadrature component n_Q (t) is negligible?

(b) Suppose that k_a is adjusted relative to the message signal m (t) such that the probability of the event A_c [1 + k_a m (t)] + n₁ (t) < 0 is equal to δ_. What is the probability that the approximation y (t) = A_c [1 + k_a m (t)] = n₁ (t) is valid?

(c) Comment on the significance of the result ion part (b) for the case when δ₁ and δ₂ are both small compared with unity.