Consider a pole-zero system with system function
(a) Sketch the regular and transpose direct form II realizations of the system.
(b) Determine and sketch the type 1 and type 2 state-space realizations.
(c) Determine the impulse response of the system by inverting H(z) and by using state-space techniques.
(d) Determine the coupled-form state-space realization.
(e) Repeat parts (a) through (d) for the system obtained by changing the angle of the poles from π/3 to π/4.