Given two independent 1st order recursive systems with complex constant coefficients as described inthe figures below, determine the following:+10.8e ju/40.8e ja/4hi(n)h2(n)1. Z-transforms of h1(n) and h2(n)2. Simplified (compressed) rational Z-transform H(z) if the two systems are connected in parallel3. Simplified (compressed) rational Z-transform H(z) if the two systems are connected in series

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Answered: Given two independent 1st order…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter6: Power Flows

Section: Chapter Questions

Problem 6.16P

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1. If a system function has zeros at the origin of the z-plane then the system function is a properrational function. Why? 2. Can you obtain the z-transform of u[n] at z = 0? If you can, what is its value? If you cannot,why not? 3. What is the preferred method for obtaining the inverse z-transform of rational functions?Describe this method. 4. Explain why a one-sided z-transform is able to determine response to a LCCDE with initialconditions while the two-sided z-transform cannot. 5. Can any system with a rational system function be decomposed into a product of an allpasssystem and a minimum-phase system? If yes, then explain how?
Given K(W,X,Y,Z) = Σm(3,4,13,15) + Σd(1,2,5,6,8,10,12,14) 1. Determine the minimal Sum of Products (SOP) expression using a Karnaugh Map. 2. Determine the minimal Product of Sums (POS) expression using a Karnaugh Map.
F(ABC) = πM(0, 1, 3, 6) 1. Derive the minimal sum of product (SOP) form of F using a K-map 2. Derive the minimal product of sum (POS) form of F using a K-map 3. Calculate the literal cost of the minimal POS and SOP form
For each of the following z-domain functions, determine the (causal) sampled time function using the z-transform tables of one-sided z-transform transform pairs and attributes. Assume the one-sided z-transform requires a Region of Convergence of |z| > 1.
Which of the following is not a requirement for the Routh stability test? a. all coefficients positive b. even-degree polynomial c. polynomial characteristic equation d. terms arranged in standard order
1-What are static error coefficients? how will you calculate the steady state error using static error coefficients? (Write equations also, about kp, Kv, Ka) 2-Explain, how will you calculate the steady state error in Laplace domain?
c) Obtain Z-transform of (1-e-Ts )/s(1/s+1) d) The z-transform X (z) of a function X (k), is given by;X (z) =z(0.1065z +0.09021)/(z-1)(z2-1.5z+0.6967) Determine an expression for X (k), by finding the inverse z-transform function of X(z)
G(WXYZ) = Σm(0,2,8,10,14,15) 1. Derive the minimal sum of product (SOP) form of G using a K-map 2. Derive the minimal product of sum (POS) form of g using a K-map 3. Calculate the literal cost of the minimal POS and SOP form
a) Based on your understanding, describe the use of Laplace-transform and z-transform in linear time invariant analysis.b) Find Laplace transform and sketch the associated ROC of following function,i. ?(?)=(?+1)?−??(?)ii. ?(?)=?−2?[?(?)−?(?−4)].c) Find z-transform and sketch the associated ROC of following function,i) ?[?]=(23)??[?]+(16)??[?]ii) ?[?]=?3??[?]
a) The dynamics of a discrete-time system are determined by the difference equation;8yk+2 –6y+1 +yk=9Determine the response of the system given thaty0=1 and y1=1.5 b) Find the state transition matrix for the digital system given byX (k+1) = [ -1 0] x (k) [ 1 3] c) Obtain Z-transform of (1-e-Ts )/s(1/s+1) d) The z-transform X (z) of a function X (k), is given by;X (z) =z(0.1065z +0.09021)/(z-1)(z2-1.5z+0.6967) Determine an expression for X (k), by finding the inverse z-transform function of X(z)
6. Simplify the given function using K-Map. F (A, B, C, D) =∑m (0,2,3,4,6,8,10,12,14) +d (1,11,13)
Given J(a,b,c,d) = Σm(0,1,2,3,7,8,10) + Σd(5,6,11,15) 1. Determine the minimal Sum of Products (SOP) expression using a Karnaugh Map. 2. Determine the minimal Product of Sums (POS) expression using a Karnaugh Map.

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