Problem 4: [30 point(s)] Consider the following system with sampling period T = 1s. u(t) y(t) y*(t) D(z) G(S) G(s) T T 4.1 [2 point(s)] List those transfer functions in the block diagram that contain the transfer func- tion of a data hold. 4.2 [8 point(s)] Suppose D(z) = 1 G(s)G2(s) = Z s(s+1) s+2s+2 (not including data hold), u(t) = t and we use a zero-order hold. Solve for y(t) by hand. 4.3 [6 point(s)] Find the pulse transfer function of the whole system by hand. 4.4 [6 point(s)] Using the pulse transfer function, find y*(t) by hand. 4.5 [6 point(s)] Sketch by hand y(t) and y* (t). 4.6 [2 point(s)] The dc gain is defined as the steady-state output when the input is the Heaviside function. What is the dc gain of the system?