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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

Q. 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?
Verified Answer
Consider a single input single output discrete-time system with x[n] a...
For an input-output relation if the present output depends on present and past input values then the given system is “Causal”.
For the given relation,
For n ranging from 0 to 10 present output depends on present input only.
At all other points present output depends on present and past input values.
Thus the system is “Causal”.
Stability
If x[n] is bounded for the given finite range of n i.e. 0<n<10 y[n] is also bounded.
Similarly x [n] - x [n- 1] is also bounded at all other values of n
Thus the system is “stable”.
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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 asQ. Which 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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