Consider the filter shown in figure

(a) Determine its system function.

(b) Sketch the pole-zero plot and check for stability if

(1) b₀ = b₂ = 1,             b₁ = 2,  a₁ = 1.5, a₂ = - 0.9

(2) b₀ = b₂ = 1,             b₁ = 2,  a₁ = 1,   a₂ = - 2

(c) Determine the response to x(n) = cos(πn/3) if b₀ = 1, b₁ = b₂ = 0, a₁ = 1, and a₂ = - 0.99.

X(n) bo b2 ytn)