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Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
Which one of the following statements is true about the system?
Which one of the following statements is true about the system?
- a)It is causal and stable
- b)It is causal but not stable
- c)It is not causal but stable
- d)It is neither causal nor stable
Correct answer is option 'A'. Can you explain this answer?
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Consider a single input single output discrete-time system with x[n] a...
Condition for Causality of LTI System:
In time domain, a system is causal when the output does not depend on any future input (i.e. depends only on present or past input).
Condition for BIBO Stability of LTI System:
In time domain, a system is stable when the output is bounded for the bounded input. (note- Bounded input means the input for which it has a finite value for all time)
Now, we check the given input-output relation:
y[n]= n |x[n]| for 0≤n≤10
x[n] – x[n-1] otherwise
For the given relation, the output depends only on the present input for 0≤n≤10 and for other time duration, the output depends on present input and past input. So, the system output does not depend on the future input, hence the system is causal.
For 0≤n≤10, output is the multiple of given input and time n. As n is finite, the output will also be finite (bounded) for a given finite input (bounded input). So, the system is stable for the duration 0≤n≤10. Again, for other duration, output is difference of the present input x[n] and past input x[n-1]. So, the output will always be finite (bounded), if input x[n] and x[n-1] are finite (bounded input). Hence, the system is BIBO stable for this region also. Thus, the given system is BIBO stable.
Hence, we conclude that system is both causal and BIBO stable.
Option (A) is correct.
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Consider a single input single output discrete-time system with x[n] a...
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Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related asWhich one of the following statements is true about the system?a)It is causal and stableb)It is causal but not stablec)It is not causal but stabled)It is neither causal nor stableCorrect answer is option 'A'. Can you explain this answer?
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