Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > Assertion (A): The system functionH(z) = z3-2...
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Assertion (A): The system function
H(z) = z3-2z2+z/z2+1/4z+1/s is not causal
Reason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.
H(z) = z3-2z2+z/z2+1/4z+1/s is not causal
Reason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.
- a)Both A and R are true and R is correct explanation of A
- b)Both A and R are true and R is not correct Explanation of A
- c)A is True and R is false
- d)A is False and R is true
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not c...
Explanation: The transfer function is not causal as for causality the numerator of H (z) is of lower order than the denominator, the system may be causal.
Most Upvoted Answer
Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not c...
Assertion (A): The system function H(z) = z^3-2z^2 z/z^2 1/4z 1/s is not causal.
Reason (R): If the numerator of H(z) is of lower order than the denominator, the system may be causal.
Explanation:
To determine whether the system function H(z) is causal or not, we need to analyze its numerator and denominator.
The numerator of H(z) is z^3-2z^2 z, which can be rewritten as z^3 - 2z^3 = -z^3.
The denominator of H(z) is z^2 1/4z 1/s, which can be simplified to z^2 + 1/4s.
Based on the definition of a causal system, a system is causal if and only if its impulse response h[n] is equal to zero for n < />
The impulse response h[n] of a system can be obtained by taking the inverse Z-transform of the system function H(z). In this case, we are given the system function H(z), so we can directly analyze it.
The inverse Z-transform of H(z) can be obtained by performing partial fraction decomposition. However, in order to determine causality, we only need to analyze the poles of H(z).
The poles of H(z) are the values of z that make the denominator of H(z) equal to zero. In this case, the poles are z = 0 and z = -1/4s.
Since there is a pole at z = 0, the system is not causal. This is because for a causal system, all the poles of H(z) must be inside the unit circle in the z-plane.
Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Reason (R): If the numerator of H(z) is of lower order than the denominator, the system may be causal.
Explanation:
To determine whether the system function H(z) is causal or not, we need to analyze its numerator and denominator.
The numerator of H(z) is z^3-2z^2 z, which can be rewritten as z^3 - 2z^3 = -z^3.
The denominator of H(z) is z^2 1/4z 1/s, which can be simplified to z^2 + 1/4s.
Based on the definition of a causal system, a system is causal if and only if its impulse response h[n] is equal to zero for n < />
The impulse response h[n] of a system can be obtained by taking the inverse Z-transform of the system function H(z). In this case, we are given the system function H(z), so we can directly analyze it.
The inverse Z-transform of H(z) can be obtained by performing partial fraction decomposition. However, in order to determine causality, we only need to analyze the poles of H(z).
The poles of H(z) are the values of z that make the denominator of H(z) equal to zero. In this case, the poles are z = 0 and z = -1/4s.
Since there is a pole at z = 0, the system is not causal. This is because for a causal system, all the poles of H(z) must be inside the unit circle in the z-plane.
Therefore, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
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Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.a)Both A and R are true and R is correct explanation of Ab)Both A and R are true and R is not correct Explanation of Ac)A is True and R is falsed)A is False and R is trueCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.a)Both A and R are true and R is correct explanation of Ab)Both A and R are true and R is not correct Explanation of Ac)A is True and R is falsed)A is False and R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.a)Both A and R are true and R is correct explanation of Ab)Both A and R are true and R is not correct Explanation of Ac)A is True and R is falsed)A is False and R is trueCorrect answer is option 'A'. Can you explain this answer?.
Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.a)Both A and R are true and R is correct explanation of Ab)Both A and R are true and R is not correct Explanation of Ac)A is True and R is falsed)A is False and R is trueCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2026 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.a)Both A and R are true and R is correct explanation of Ab)Both A and R are true and R is not correct Explanation of Ac)A is True and R is falsed)A is False and R is trueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): The system functionH(z) = z3-2z2+z/z2+1/4z+1/s is not causalReason (R): If the numerator of H (z) is of lower order than the denominator, the system may be causal.a)Both A and R are true and R is correct explanation of Ab)Both A and R are true and R is not correct Explanation of Ac)A is True and R is falsed)A is False and R is trueCorrect answer is option 'A'. Can you explain this answer?.
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