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The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. What is the value of the step response of the system as n→∞?
- a)1/(1+a)
- b)1/(1-a)
- c)a/(1+a)
- d)a/(1-a)
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. ...
Explanation: The step response of the system is y(n)=x(n)*h(n) where x(n)=u(n)
On applying z-transform on both sides, we get
On applying z-transform on both sides, we get
Most Upvoted Answer
The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. ...
The impulse response of a relaxed LTI system is given by h(n) = anu(n), where a is a constant and u(n) is the unit step function.
The unit step function u(n) is defined as:
u(n) = 1, for n >= 0
u(n) = 0, for n < />
To determine the value of |a|, we need to consider the condition for the system to be stable. For a system to be stable, the sum of the absolute values of the impulse response must be finite.
Let's calculate the sum of the absolute values of h(n):
∑ |h(n)| = ∑ |anu(n)|
Since u(n) = 1 for n >= 0, the sum can be split into two parts:
∑ |h(n)| = ∑ |an|, for n >= 0
Since the system is relaxed, the impulse response only exists for n >= 0. Therefore, the sum is infinite if |a| >= 1, and finite if |a| < />
In conclusion, for the impulse response h(n) = anu(n), the system is stable if |a| < 1.="" />
The unit step function u(n) is defined as:
u(n) = 1, for n >= 0
u(n) = 0, for n < />
To determine the value of |a|, we need to consider the condition for the system to be stable. For a system to be stable, the sum of the absolute values of the impulse response must be finite.
Let's calculate the sum of the absolute values of h(n):
∑ |h(n)| = ∑ |anu(n)|
Since u(n) = 1 for n >= 0, the sum can be split into two parts:
∑ |h(n)| = ∑ |an|, for n >= 0
Since the system is relaxed, the impulse response only exists for n >= 0. Therefore, the sum is infinite if |a| >= 1, and finite if |a| < />
In conclusion, for the impulse response h(n) = anu(n), the system is stable if |a| < 1.="" />
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The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. What is the value of the step response of the system as n→∞?a)1/(1+a)b)1/(1-a)c)a/(1+a)d)a/(1-a)Correct answer is option 'B'. Can you explain this answer?
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The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. What is the value of the step response of the system as n→∞?a)1/(1+a)b)1/(1-a)c)a/(1+a)d)a/(1-a)Correct answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. What is the value of the step response of the system as n→∞?a)1/(1+a)b)1/(1-a)c)a/(1+a)d)a/(1-a)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The impulse response of a relaxed LTI system is h(n)=anu(n),|a|<1. What is the value of the step response of the system as n→∞?a)1/(1+a)b)1/(1-a)c)a/(1+a)d)a/(1-a)Correct answer is option 'B'. Can you explain this answer?.
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