Problem 1.2 Consider the moving average filter example (1.6), but now as a fourpoint moving average filter with input u and output y. (a) Give the difference equation describing this system in terms of the relationship between u(t) and y(t) and numerically evaluate the behavior of the filter for a unit step input, such that u(t) = 1 for all t. (b) Represent the system in terms of an impulse response or convolution model and give the discrete-time pulse response, i.e., for u(t) = 1 for t = 0 and u(t) = 0 for t = 0. (c) Represent the system in state-space form. Give an alternative state-space form and check the corresponding input–output behaviors. (d) Is this system linear, time-invariant, and causal? Motivate your answer.