Part 1. Determine the inverse z-transform using partial fraction expansion that results to a causal function A. B. C. D. X(z) = 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 A. 2 B. 4 C. 5 D. None of these X(z) Z 1-52-¹ +11z-²-152-3 X(z) Z X(z) Z 52-² = = 5z z³5z²+11z - 15 5z 2-3-52-2+ 112-1-15 5 z³5z²+11z - 15 15z³-11z² + 5z - 1 The roots of the denominator of X(z)/z are 5z X(2) can be resolved into the sum of how many partial fractions? Z

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Part 1. Determine the inverse z-transform using partial fraction expansion that results to a causal
function
A.
B.
C.
D.
X(z):
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?
A. 2
B. 4
C. 5
D. None of these
= 152-¹ +11z-²-152-3
X(z)
Z
X(z)
5z
Z z³5z² + 11z - 15
=
5z-²
X(z)
Z
X(z)
Z
=
5z
2-35z²+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:Part 1. Determine the inverse z-transform using partial fraction expansion that results to a causal function A. B. C. D. X(z): 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? A. 2 B. 4 C. 5 D. None of these = 152-¹ +11z-²-152-3 X(z) Z X(z) 5z Z z³5z² + 11z - 15 = 5z-² X(z) Z X(z) Z = 5z 2-35z²+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
Z
Let p = a + jb, b> 0 be the complex root of the denominator of (2). Which of the
following is correct?
A.
B.
C.
D.
X(z)
Z
X(z)
Z
0.625 0.4419e/2.3562 0.4419e-j2.3562
Z-3
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) = -0.625.3"u(-n-1)
D. x₁ (n) = 0.625.3"u(n)
+
0.4419e/2.3562
z-p
0.625
z - 3
0.4419e/2.3562 0.4419e-j2.3562
z-p
z-p*
+
+
+
0.4419e/135
z-p
0.4419e-j2.3562
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)?
0.4419e-j135
z-p*
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)
Transcribed Image Text:Z Let p = a + jb, b> 0 be the complex root of the denominator of (2). Which of the following is correct? A. B. C. D. X(z) Z X(z) Z 0.625 0.4419e/2.3562 0.4419e-j2.3562 Z-3 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) = -0.625.3"u(-n-1) D. x₁ (n) = 0.625.3"u(n) + 0.4419e/2.3562 z-p 0.625 z - 3 0.4419e/2.3562 0.4419e-j2.3562 z-p z-p* + + + 0.4419e/135 z-p 0.4419e-j2.3562 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)? 0.4419e-j135 z-p* 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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