The system function of a communication channel is given by

H(z) = (1 – 0.9e^j0.4π z ^-1) (1 – 0.9e^-j0.4π z ^-1) (1 – 1.5e^j0.6π z ^-1) (1 – 1.5e^-j0.6π z ^-1).

Determine the system function H₀ (z) of a causal and stable compensating system so that the cascade interconnection of the two systems has a flat magnitude response. Sketch the pole-zero plots and the magnitude and phase responses of all systems involved into the analysis process.