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The discrete time system described by y(n) = [x(n)]2 is
- a)causal and linear
- b)casual and non-linear
- c)non-casual and linear
- d)non-causal and non-linear
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The discrete time system described by y(n) = [x(n)]2 isa)causal and li...
Concept:
Linearity: Necessary and sufficient condition to prove the linearity of the system is that the linear system follows the laws of superposition i.e. the response of the system is the sum of the responses obtained from each input considered separately.
y{ax1[t] + bx2[t]} = a y{x1[t]} + b y{x2[t]}
Conditions to check whether the system is linear or not.
- The output should be zero for zero input
- There should not be any non-linear operator present in the system.
Causal system:
If O/P of the system is independent of the future value of input then the system is said to be causal. Causal systems are practical or physically reliable systems.
Analysis:
y(n) = [x(n)]2
Linearity check:
x1(n) → x1(n)2
x2(n) → x2(n)2
x3(n) = [x1(n) + x2(n)] → [x1(n) + x2(n)]2 = x1(n)2 + x2(n)2 + 2x1(n) x2(n)
≠ x1(n)2 + x2(n)2
∴ Non - linear
Causality check:
y(0) = x(0)2
y(1) = x(1)2
y(-1) = x(-1)2
∴ the system is causal.
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The discrete time system described by y(n) = [x(n)]2 isa)causal and linearb)casual and non-linearc)non-casual and lineard)non-causal and non-linearCorrect answer is option 'B'. Can you explain this answer?
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