Q1) A causal system is represented by the following difference equation: y(n)=x(n) - - x(n-1)+ y(n-1) - y(n-2) a) Find the system transfer function H[z]. b) From (a) find the impulse response of the system using partial fraction. c) Find the frequency response

Problem 2 Each of the following figures shows the impulse response of a LTI system h[n]. For each figure in (a), (b), (c) and (d): (i) Firstly write an expression of h[n] and then find an expression of the frequency response of the system: h[n]e-inw (ii) say whether H(e) as a function of w is even or odd or neither (iii) and sketch/plot the magnitude of the frequency response, i.e., H(ew)|, over -27 < w 2π (you may use Matlab). (a) (b) In each figure, the value indicated for each impulse means the amplitude of that impulse. For example, if the value of an impulse at n = 3 is indicated to be 2j, it means 2jd[n – 3]. The value of h[n] is zero for all n outside the range shown in the figure. h[n] (c) H(ejw) = h[n] 1 1 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 h[n] -6 -5 -4 -3 -2 -1 0 1 -6-5-4-3-2-1 0 1 n=-∞ 1 1 1 1 1 2 3 4 5 6 2 3 4 5 6 n n h[n] is real-valued. h[n] is real-valued. h[n] is real-valued.

Ex. 449. K*G(s)=K*1/(s(s+3)(s+6)) is the FTF of a unity-feedback closed-loop system. Calculate the asymptote centroid and show it on a professional root locus plot. Draw the asymptote plot separately. Determine the break-away point and K at the break-away point and show both on the plots. Formal documentation required. ans: 3

x(n) hi(n)-0.5u(п) w(n) h2(n)=2"u(n) y(n)