In this problem, you will consider three different LTI systems. All three are causal and have real impulse responses. You will be given additional information about each system. Using this information, state as much as possible about the poles and zeros of each system function and about the length of the impulse response of the system,

(a) H₁(z) has a pole at z = 0.9e^jπ/3, and when x[n] = u[n], lim _n→∞ y[n] = 0.

(b) H₂(z) has a zero at z = 0.8e^jπ/4, H₂(e^jω) has linear phase with < H₂(e^jω) = −2.5ω, and 20 log₁₀ |H₂(e^j0)| = −∞.

(c) H₃(z) has a pole at z = 0.8e^jπ/4 and |H₃(e^jω)| = 1 for all ω.