(30 points) System properties. (a) (20 points) A system with input x(t) and output y(t) can be time-invariant, causal or stable. Determine which of these properties hold for each of the following systems. Explain your answer. i. y(t) = |x(t)| + x(2t) ii. y(t) = t+T tT x()d, where T is positive and constant. iii. y(t) = (t + 1) t x()d iv. y(t) = 1+x(t)cos(t) v. y(t) = 1 1+x2(t) (b) (6 points) Consider the following three systems: S1 : w(t) = x(t/2) t S2 : z(t) = w()d S3 : y(t) = S3(z(t)) The three systems are connected in series as illustrated here: Choose the third system S3, such that overall system is equivalent to the following system: t1 y(t) = x()d