7.2. A discrete-time signal x[n] has z-transform X(z) = 8z² - Z 2z - 1 Determine the z-transform V(z) of the following signals: - - (a) v[n] = x[n = 4]u[n = 4] (b) v[n] = x[n + 2]u[n + 2] (c) v[n] = cos(2n)x[n] (d) v[n] = e³n x[n] (e) v[n] = n²x[n] (f)_v[n] = x[n]*x[n]

Draw the block diagram representation of direct form I and direct form II of the followingtransfer functions:

Transformation

5. a. Convert the following expressions into a sum-of-products (SOP) form: (A +B)(C+B) (A +BC)C b. Cany out the following computations in 2's complement: i. 27-21 ii. 35-43

23. Convert the following expressions to sum-of-product (SOP) forms: a. (A + B) (C+B) 24. Convert the following expressions to sum-of-product (SOP) forms: a. AB + CD (AB + CD)

H.w. Derive a second order DE for the curvent i(t) tigure (4). as skown in R

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Find the inverse Z-Transform for X(Z) shown below for ROC 1- 03 * 22 – 4z - X(Z) = (2 – 1)(22 – 52 + 6) 1 Add file Find the Z-transform for x(n) shown below including ROC * a(n) = (-)"sin(-n)u(n) 1 Add file

The following plot is a step response of a sixth order system. 1. Find the time domain specifications i.e. Tp. Tri. T. and P.O. 2. Find a second order system whose response matches the given response in the following sense a. The percentage overshoot and rise time b. The peak time and settling time c. The rise time and settling time You have to find three systems Aroude 1 14 13) 12 UP E ON ST 06 0.5 DA 03 63 DI 0 6 A W . -CA P.O.= e √1-2 Ts= 4 ζωη Satisfying 2% criteria 10 Control Systems Homework Problem 3 100 M 16 18 20 Step Response for 24 21 20 30 The P.O. -In (100) √²+In² (²00) Tr Tp 2.16+0.60 On 0.3<≤0.8 Onv T 1-32 and 10% to 90% value

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