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)
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd035b2ee-d0be-4d62-a917-507070148a16%2F2c6a48ec-f5da-4538-a72f-6ae8dc5722ec%2Frea361_processed.png&w=3840&q=75)
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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