Consider the fist-order transfer function Y(s)/U(s) = l/(s +1). Generate a set of data (t = 1,2, . . . 20) by integrating this equation for u = 1 and randomly adding binary noise to the output, ±0.05 units at each integer value of t. Design a digital filter for this system and compare the filtered and noise-free step responses for t =1. Justify your choice of τF. Repeat for other noise levels, for example, ±0.01 and 0.1.