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An LTI system is causal if and only if
- a)h(t) = 0 for t < 0
- b)h(t) is finite for 0 < t < ∞
- c)h(t) is finite for t < 0
- d)h(t) is non-zero for all t
Correct answer is option 'A'. Can you explain this answer?
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An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is...
The impulse response is the output of a system when the input is an impulse, i.e.
The impulse response of a system can be used to evaluate various system properties. Causality is one such property, that states, “if the output of the system at any time depends only on the past and present values of the input, the system is said to be causal.”
If the impulse response is known, the system is said to be causal, if h(t) = 0 for t < 0.
Examples:
System (1) is causal
The impulse response of a system can be used to evaluate various system properties. Causality is one such property, that states, “if the output of the system at any time depends only on the past and present values of the input, the system is said to be causal.”
If the impulse response is known, the system is said to be causal, if h(t) = 0 for t < 0.
Examples:
System (1) is causal
System (2) is non-causal, as h(t) ≠ 0 for t < 0.
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An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is...
Understanding Causality in LTI Systems
In Linear Time-Invariant (LTI) systems, causality is a crucial property that determines how the system responds to inputs over time.
Definition of Causality
- An LTI system is considered causal if the output at any time depends only on present and past inputs, not future inputs.
Impulse Response and Causality
- The impulse response of an LTI system, denoted as h(t), plays a vital role in defining its behavior.
Key Point: Causal Impulse Response
- For a system to be causal, it must satisfy the condition:
- h(t) = 0 for t < />
- This means that the system does not react to any input that occurs before time zero.
Reasoning Behind Option A
- If h(t) is zero for t < />
- The system's output at any given time depends solely on the current and past inputs.
- It ensures that the system does not produce an output based on future signals, aligning with the definition of causality.
Rejection of Other Options
- Option B: h(t) is finite for 0 < t="" />< />
- This does not guarantee causality; the system could still respond to future inputs.
- Option C: h(t) is finite for t < />
- This contradicts the definition of a causal system, as it implies a response to past inputs.
- Option D: h(t) is non-zero for all t.
- This could imply the system responds to future inputs, violating causality.
Conclusion
- Therefore, the correct answer is Option A: h(t) = 0 for t < 0,="" which="" is="" the="" defining="" characteristic="" of="" a="" causal="" lti="" system.="" 0,="" which="" is="" the="" defining="" characteristic="" of="" a="" causal="" lti="" />
In Linear Time-Invariant (LTI) systems, causality is a crucial property that determines how the system responds to inputs over time.
Definition of Causality
- An LTI system is considered causal if the output at any time depends only on present and past inputs, not future inputs.
Impulse Response and Causality
- The impulse response of an LTI system, denoted as h(t), plays a vital role in defining its behavior.
Key Point: Causal Impulse Response
- For a system to be causal, it must satisfy the condition:
- h(t) = 0 for t < />
- This means that the system does not react to any input that occurs before time zero.
Reasoning Behind Option A
- If h(t) is zero for t < />
- The system's output at any given time depends solely on the current and past inputs.
- It ensures that the system does not produce an output based on future signals, aligning with the definition of causality.
Rejection of Other Options
- Option B: h(t) is finite for 0 < t="" />< />
- This does not guarantee causality; the system could still respond to future inputs.
- Option C: h(t) is finite for t < />
- This contradicts the definition of a causal system, as it implies a response to past inputs.
- Option D: h(t) is non-zero for all t.
- This could imply the system responds to future inputs, violating causality.
Conclusion
- Therefore, the correct answer is Option A: h(t) = 0 for t < 0,="" which="" is="" the="" defining="" characteristic="" of="" a="" causal="" lti="" system.="" 0,="" which="" is="" the="" defining="" characteristic="" of="" a="" causal="" lti="" />
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An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. 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 An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. 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 An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. Can you explain this answer?.
An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. 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 An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. 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 An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. Can you explain this answer?.
Solutions for An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of An LTI system is causal if and only ifa)h(t) = 0 for t < 0b)h(t) is finite for 0 < t < ∞c)h(t) is finite for t < 0d)h(t) is non-zero for all tCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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