Part 1. Determine the inverse z-transform using partial fraction expansion that results to a causal function X(z) 5z-2 1 - 5z-1 +11z-2-15z-3 Which of the following is correct?
Part 1. Determine the inverse z-transform using partial fraction expansion that results to a causal function X(z) 5z-2 1 - 5z-1 +11z-2-15z-3 Which of the following is correct?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer 1 Only
Transcribed Image Text:Part 1. Determine the inverse z-transform using partial fraction expansion that results to a causal
function
1.
A.
B.
C.
D.
X(z)
2.
A. -3,1-j2 and - 1 + j2
B. 3,1 + j2 and 1-j2
C. 1+ j2 and 1-j2
D. -2 + j2 and -2-j
Which of the following is correct?
X(z)
Z
3
A. 2
B. 4
C. 5
D. None of these
X(z)
Z
=
X(z)
Z
X(z)
Z
52-2
15z-1 +11z-2-15z-3
=
5z
z35z² + 11z - 15
5z
z-35z2+11z-¹-15
5
z³5z² + 11z - 15
5z
The roots of the denominator of X(z)/z are
15z311z2 + 5z - 1
X(z)
can be resolved into the sum of how many partial fractions?
Z
Transcribed Image Text:4.
following is correct?
A.
B.
C.
Let p = a + jb, b > 0 be the complex root of the denominator of *(2). Which of the
X(z)
Z
D.
X(z)
Z
X(z)
Z
=
=
0.625 0.4419e/2.3562 0.4419e-12.3562
z-p
z-p*
X(z)
Z
0.625
z + 3
X(z)
Z
=
+
5.
A. x₁ (n) = 0.625.3-"u(n)
B. x₁(n) = 0.625 (-3)"u(-n-1)
C. x₁(n) = -0.625 · 3¹u(n − 1)
D. x₁ (n) = 0.625.3"u(n)
0.4419e/2.3562
z-p
0.4419e/2.3562
z-p
0.625 0.4419e/135
z-3
Z-P
+
+
0.4419e-12.3562
z-p
0.4419e-12.3562
z-p*
+
0.4419e-j135
z-p
For nos. 5 and 6, let x(n) = x₁(n) + x₂ (n), where x₂ (n) contains the sinusoidal term.
Which of the following is equal to x₁ (n)?
6.
Which of the following is equal to x₂ (n)?
A. x₂ (n) = 2√5(0.4419) cos(1.1071 +2.3562n) u(n − 1)
B. x₂ (n) = 2√5(0.625)" cos(1.1071 +135n) u(−n − 1)
C. x₂ (n) = 2(0.4419)(√5) cos(1.1071n +2.3562)u(n)
D. x₂ (n) = 2(2.3562)(1.1071) cos(1.1071 +2.3562n) u(n)
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