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An LTI system is said to be causal if and only if
- a)Impulse response is non-zero for positive values of n
- b)Impulse response is zero for positive values of n
- c)Impulse response is non-zero for negative values of n
- d)Impulse response is zero for negative values of n
Correct answer is option 'D'. Can you explain this answer?
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An LTI system is said to be causal if and only ifa)Impulse response is...
Explanation: Let us consider a LTI system having an output at time n=n0given by the convolution formula
=(h(0)x(n0)+h(1)x(n0-1)+h(2)x(n0-2)+….)+(h(-1)x(n0+1)+h(-2)x(n0+2)+…)
As per the definition of the causality, the output should depend only on the present and past values of the input. So, the coefficients of the terms x(n0+1), x(n0+2)…. should be equal to zero.
that is, h(n)=0 for n<0 .
As per the definition of the causality, the output should depend only on the present and past values of the input. So, the coefficients of the terms x(n0+1), x(n0+2)…. should be equal to zero.
that is, h(n)=0 for n<0 .
Most Upvoted Answer
An LTI system is said to be causal if and only ifa)Impulse response is...
Causal LTI system and Impulse response
A Linear Time-Invariant (LTI) system is said to be causal if the output of the system at any instant of time depends only on the present and past values of the input signal. In other words, the output of a causal system cannot depend on the future values of the input signal.
The impulse response of an LTI system is the response of the system to an impulse input. An impulse input is a signal that has a value of 1 at time t=0 and is zero everywhere else. The impulse response of a system is a very important characteristic of the system, as it provides a complete description of the system's behavior.
Impulse response and causality
The impulse response of a causal LTI system must be zero for negative values of time. This is because the output of the system at any time t depends only on the present and past values of the input signal. If the impulse response is non-zero for negative values of time, it means that the output of the system at time t depends on the future values of the input signal, which violates the definition of a causal system.
Therefore, option D is the correct answer - An LTI system is said to be causal if and only if the impulse response is zero for negative values of n.
Examples of causal and non-causal systems
Examples of causal systems include:
- A low-pass filter that removes high-frequency components from a signal.
- A delay line that introduces a delay between the input and output signals.
Examples of non-causal systems include:
- A filter that predicts the future values of the input signal.
- A system that uses feedback to generate its output signal.
A Linear Time-Invariant (LTI) system is said to be causal if the output of the system at any instant of time depends only on the present and past values of the input signal. In other words, the output of a causal system cannot depend on the future values of the input signal.
The impulse response of an LTI system is the response of the system to an impulse input. An impulse input is a signal that has a value of 1 at time t=0 and is zero everywhere else. The impulse response of a system is a very important characteristic of the system, as it provides a complete description of the system's behavior.
Impulse response and causality
The impulse response of a causal LTI system must be zero for negative values of time. This is because the output of the system at any time t depends only on the present and past values of the input signal. If the impulse response is non-zero for negative values of time, it means that the output of the system at time t depends on the future values of the input signal, which violates the definition of a causal system.
Therefore, option D is the correct answer - An LTI system is said to be causal if and only if the impulse response is zero for negative values of n.
Examples of causal and non-causal systems
Examples of causal systems include:
- A low-pass filter that removes high-frequency components from a signal.
- A delay line that introduces a delay between the input and output signals.
Examples of non-causal systems include:
- A filter that predicts the future values of the input signal.
- A system that uses feedback to generate its output signal.
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An LTI system is said to be causal if and only ifa)Impulse response is non-zero for positive values of nb)Impulse response is zero for positive values of nc)Impulse response is non-zero for negative values of nd)Impulse response is zero for negative values of nCorrect answer is option 'D'. Can you explain this answer?
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An LTI system is said to be causal if and only ifa)Impulse response is non-zero for positive values of nb)Impulse response is zero for positive values of nc)Impulse response is non-zero for negative values of nd)Impulse response is zero for negative values of nCorrect answer is option 'D'. 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 An LTI system is said to be causal if and only ifa)Impulse response is non-zero for positive values of nb)Impulse response is zero for positive values of nc)Impulse response is non-zero for negative values of nd)Impulse response is zero for negative values of nCorrect answer is option 'D'. 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 An LTI system is said to be causal if and only ifa)Impulse response is non-zero for positive values of nb)Impulse response is zero for positive values of nc)Impulse response is non-zero for negative values of nd)Impulse response is zero for negative values of nCorrect answer is option 'D'. Can you explain this answer?.
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