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Whether the system described by the input-output equations y(n)=x(n)-x(n-1) a Time-variant system?
- a)True
- b)False
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Whether the system described by the input-output equations y(n)=x(n)-x...
Explanation: If the input is delayed by k units then the output will be y(n,k)=x(n-k)-x(n-k-1)
If the output is delayed by k units then y(n-k)=x(n-k)-x((n-k)-1)
=>y(n,k)=y(n-k). Hence the system is time-invariant.
If the output is delayed by k units then y(n-k)=x(n-k)-x((n-k)-1)
=>y(n,k)=y(n-k). Hence the system is time-invariant.
Most Upvoted Answer
Whether the system described by the input-output equations y(n)=x(n)-x...
Input-Output Equations
The input-output equations for the system are:
- y(n) = x(n) - x(n-1)
where x(n) is the input signal at time n and y(n) is the output signal at time n.
Time-Variant System
A time-variant system is a system whose output depends on both the input signal and the time at which the input signal is applied. In other words, the system's behavior changes with time.
Analysis
In the given input-output equation, the output signal y(n) depends only on the current input signal x(n) and the past input signal x(n-1). The output is not dependent on the current time n, which means that the behavior of the system does not change with time. Therefore, the system described by the input-output equation y(n) = x(n) - x(n-1) is a time-invariant system.
Conclusion
Hence, we can conclude that the correct option is 'B' i.e. False. The system described by the input-output equation y(n) = x(n) - x(n-1) is a time-invariant system.
The input-output equations for the system are:
- y(n) = x(n) - x(n-1)
where x(n) is the input signal at time n and y(n) is the output signal at time n.
Time-Variant System
A time-variant system is a system whose output depends on both the input signal and the time at which the input signal is applied. In other words, the system's behavior changes with time.
Analysis
In the given input-output equation, the output signal y(n) depends only on the current input signal x(n) and the past input signal x(n-1). The output is not dependent on the current time n, which means that the behavior of the system does not change with time. Therefore, the system described by the input-output equation y(n) = x(n) - x(n-1) is a time-invariant system.
Conclusion
Hence, we can conclude that the correct option is 'B' i.e. False. The system described by the input-output equation y(n) = x(n) - x(n-1) is a time-invariant system.
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Whether the system described by the input-output equations y(n)=x(n)-x(n-1) a Time-variant system?a)Trueb)FalseCorrect answer is option 'B'. Can you explain this answer?
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