Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > What is the partial fraction expansion of the...
Start Learning for Free
What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2 )?
- a)2z/(z-1)-z/(z+0.5)
- b)2z/(z-1)+z/(z-0.5)
- c)2z/(z-1)+z/(z+0.5)
- d)2z/(z-1)-z/(z-0.5)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the partial fraction expansion of the proper function X(z)= 1/...
Explanation: First we eliminate the negative powers of z by multiplying both numerator and denominator by z2.
Thus we obtain X(z)= z2/(z2-1.5z+0.5)
The poles of X(z) are p1=1 and p2=0.5. Consequently, the expansion will be
(X(z))/z = z/((z-1)(z-0.5)) = 2/((z-1) ) – 1/((z-0.5) )( obtained by applying partial fractions)
=>X(z)= 2z/(z-1)-z/(z-0.5).
Thus we obtain X(z)= z2/(z2-1.5z+0.5)
The poles of X(z) are p1=1 and p2=0.5. Consequently, the expansion will be
(X(z))/z = z/((z-1)(z-0.5)) = 2/((z-1) ) – 1/((z-0.5) )( obtained by applying partial fractions)
=>X(z)= 2z/(z-1)-z/(z-0.5).
Most Upvoted Answer
What is the partial fraction expansion of the proper function X(z)= 1/...
Partial Fraction Expansion of X(z)
The partial fraction expansion of a rational function is a representation of the function as a sum of simpler fractions. In this case, we want to find the partial fraction expansion of X(z) = 1/(1 - 1.5z^-1 + 0.5z^-2).
Step 1: Factor the denominator
We start by factoring the denominator of X(z): 1 - 1.5z^-1 + 0.5z^-2 = (1 - z^-1)(1 - 0.5z^-1).
Step 2: Write the partial fraction expansion
We can now write X(z) as a sum of two simpler fractions:
X(z) = A/(1 - z^-1) + B/(1 - 0.5z^-1)
where A and B are constants to be determined.
Step 3: Find the constants A and B
To find the constants A and B, we need to multiply both sides of the equation above by the common denominator:
X(z)(1 - z^-1)(1 - 0.5z^-1) = A(1 - 0.5z^-1) + B(1 - z^-1)
Simplifying this equation, we get:
X(z) = A + B - (A/2)z^-1 - (B/2)z^-1
Comparing the coefficients of z^-1 on both sides, we get:
- A/2 - B/2 = -1.5
- A/2 + B/2 = 0.5
Solving for A and B, we get:
A = -2/(1 - 0.5) = -4
B = 2/(1 - 1) = 2
Therefore, the partial fraction expansion of X(z) is:
X(z) = -4/(1 - z^-1) + 2/(1 - 0.5z^-1)
which can be simplified as:
X(z) = 2z/(z - 1) - z/(z - 0.5)
Therefore, the correct answer is option D: 2z/(z - 1) - z/(z - 0.5).
The partial fraction expansion of a rational function is a representation of the function as a sum of simpler fractions. In this case, we want to find the partial fraction expansion of X(z) = 1/(1 - 1.5z^-1 + 0.5z^-2).
Step 1: Factor the denominator
We start by factoring the denominator of X(z): 1 - 1.5z^-1 + 0.5z^-2 = (1 - z^-1)(1 - 0.5z^-1).
Step 2: Write the partial fraction expansion
We can now write X(z) as a sum of two simpler fractions:
X(z) = A/(1 - z^-1) + B/(1 - 0.5z^-1)
where A and B are constants to be determined.
Step 3: Find the constants A and B
To find the constants A and B, we need to multiply both sides of the equation above by the common denominator:
X(z)(1 - z^-1)(1 - 0.5z^-1) = A(1 - 0.5z^-1) + B(1 - z^-1)
Simplifying this equation, we get:
X(z) = A + B - (A/2)z^-1 - (B/2)z^-1
Comparing the coefficients of z^-1 on both sides, we get:
- A/2 - B/2 = -1.5
- A/2 + B/2 = 0.5
Solving for A and B, we get:
A = -2/(1 - 0.5) = -4
B = 2/(1 - 1) = 2
Therefore, the partial fraction expansion of X(z) is:
X(z) = -4/(1 - z^-1) + 2/(1 - 0.5z^-1)
which can be simplified as:
X(z) = 2z/(z - 1) - z/(z - 0.5)
Therefore, the correct answer is option D: 2z/(z - 1) - z/(z - 0.5).
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Top Courses for Electrical Engineering (EE)View all
Question Description
What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer?.
What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer?.
Solutions for What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the partial fraction expansion of the proper function X(z)= 1/(1-1.5z-1+0.5z-2)?a)2z/(z-1)-z/(z+0.5)b)2z/(z-1)+z/(z-0.5)c)2z/(z-1)+z/(z+0.5)d)2z/(z-1)-z/(z-0.5)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup