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The impulse response of a continuous time system is given by h (t) = d (t – 1) + d (t – 3).The value of the step response at t = 2 is
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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The impulse response of a continuous time system is given by h (t) = d...
Step response = integration of impulse response
So at t = 2, y(t) = 1
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So at t = 2, y(t) = 1
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The impulse response of a continuous time system is given by h (t) = d...
Impulse Response
The impulse response of a continuous-time system represents the system's output when an impulse (delta function) is applied as the input. In this case, the impulse response is given by h(t) = δ(t – 1) * δ(t – 3), where δ(t) is the delta function.
Delta Function
The delta function δ(t – a) is defined as zero for all t ≠ a, and infinite at t = a such that the integral of δ(t – a) over any interval containing a is equal to 1. In other words, δ(t – a) represents an impulse of unit area at t = a.
Step Response
The step response of a system represents the output when a unit step function is applied as the input. It can be obtained by integrating the impulse response over time.
Calculating the Step Response
To find the step response at t = 2, we integrate the impulse response over the interval [0, 2]:
∫[0,2] h(t) dt = ∫[0,2] δ(t – 1) * δ(t – 3) dt
Since δ(t – 1) is non-zero only when t = 1, and δ(t – 3) is non-zero only when t = 3, the integral becomes:
∫[0,2] δ(t – 1) * δ(t – 3) dt = ∫[0,2] 0 dt = 0
Therefore, the step response at t = 2 is 0.
Answer
The correct answer is option 'B', which is 0.
The impulse response of a continuous-time system represents the system's output when an impulse (delta function) is applied as the input. In this case, the impulse response is given by h(t) = δ(t – 1) * δ(t – 3), where δ(t) is the delta function.
Delta Function
The delta function δ(t – a) is defined as zero for all t ≠ a, and infinite at t = a such that the integral of δ(t – a) over any interval containing a is equal to 1. In other words, δ(t – a) represents an impulse of unit area at t = a.
Step Response
The step response of a system represents the output when a unit step function is applied as the input. It can be obtained by integrating the impulse response over time.
Calculating the Step Response
To find the step response at t = 2, we integrate the impulse response over the interval [0, 2]:
∫[0,2] h(t) dt = ∫[0,2] δ(t – 1) * δ(t – 3) dt
Since δ(t – 1) is non-zero only when t = 1, and δ(t – 3) is non-zero only when t = 3, the integral becomes:
∫[0,2] δ(t – 1) * δ(t – 3) dt = ∫[0,2] 0 dt = 0
Therefore, the step response at t = 2 is 0.
Answer
The correct answer is option 'B', which is 0.
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The impulse response of a continuous time system is given by h (t) = d (t – 1) + d (t – 3).The value of the step response at t = 2 isa)0b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?
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