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Q1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n)

Q1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Q1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n) d) 4(0.8) "cos (0.1лn)u(n) Q2 Given the two sequences x₁(n)= -28(n)+58(n-2) and x2(n)= 48(n-4) a) Let x3(n) = x₁(n) * x2 (n) Determine the Z transform of x3(n) b) Find x3(n) using the inverse transform of X3(z). Q3 Using the Z-transform properties and the Z-transform table find the inverse Z- transform for each of the following sequences a) 5- (7z/z+1) - (3z/z-0.5) b) (-3z/(z-0.5)) +[ 8z/(z−0.8)]+ [2z/(z-0.8)²] c) 3z/(z²+1.414z+1) d) (5z %/z-1)-[ z^²/(z−1)²] + [z −¹⁰0] + [z ³/z-0.75] Q4 Use partial fraction expansion, Find the inverse Z-transform of the following: a) [1/(z²+0.5z+0.06)] b) z/[(z+0.3)(z-0.5)] c) 5z/[(z-0.75) (z²-z+0.5)] d) 2z(z-0.4)/[(z-0.2)²(z+0.8)] Q5 A system is described by the following difference equation y(n)-0.5y(n-1) +0.06y(n-2)= (0.4)n-1u(n-1) Determine the solution when the initial conditions are y(-1) = 1 and y(-2)=2.
Transcribed Image Text:Q1 Find the z transform for each of the following sequences: a) 3u(n-4) b) 2(-0.5)nu(n) c) 4e-2nu(n) d) 4(0.8) "cos (0.1лn)u(n) Q2 Given the two sequences x₁(n)= -28(n)+58(n-2) and x2(n)= 48(n-4) a) Let x3(n) = x₁(n) * x2 (n) Determine the Z transform of x3(n) b) Find x3(n) using the inverse transform of X3(z). Q3 Using the Z-transform properties and the Z-transform table find the inverse Z- transform for each of the following sequences a) 5- (7z/z+1) - (3z/z-0.5) b) (-3z/(z-0.5)) +[ 8z/(z−0.8)]+ [2z/(z-0.8)²] c) 3z/(z²+1.414z+1) d) (5z %/z-1)-[ z^²/(z−1)²] + [z −¹⁰0] + [z ³/z-0.75] Q4 Use partial fraction expansion, Find the inverse Z-transform of the following: a) [1/(z²+0.5z+0.06)] b) z/[(z+0.3)(z-0.5)] c) 5z/[(z-0.75) (z²-z+0.5)] d) 2z(z-0.4)/[(z-0.2)²(z+0.8)] Q5 A system is described by the following difference equation y(n)-0.5y(n-1) +0.06y(n-2)= (0.4)n-1u(n-1) Determine the solution when the initial conditions are y(-1) = 1 and y(-2)=2.
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