Consider the system
y(n) = 0.875y(n – 1) – 0.125y(n – 2) + x(n)
(a) Compute its poles and design the cascade realization of the system.
(b) Quantize the coefficients of the system using truncation, maintaining a sign bit plus three other bits. Determine the poles of the resulting system.
(c) Repeat part (b) for the same precision using rounding.
(d) Compare the poles obtained in parts (b) and (c) with those in part (a). Which realization is better? Sketch the frequency responses of the systems in parts (a), (b) and (c).