An input to a 6-level quantizer has the probability density function f(X) as shown in the figure. Decision boundaries of the quantizer are chosen so as to maximize the entropy of the quantizer output. It is given that 3 consecutive decision boundaries are ‘-1’, ‘0’ and ‘1’.

Assuming that the reconstruction levels of the quantizer are the mid-points of the decision boundaries, the ratio of signal power to quantization noise power is

A Hilbert transformer is a

The open-loop transfer function of a plant is given as $$G(s) = {1 \over {{s^2} - 1}}.$$ If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is

A control system with a PD controller is shown in the figure. If the velocity error constant $${K_v} = 1000$$ and the damping ratio $$\zeta = 0.5,$$ then the values of $${K_P}$$ and $${K_D}$$ are