Discussion :: Signals and Systems
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The continuous time system described by the equation y(t) = x(t2) comes under which category
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A.
causal, linear and time varying
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B.
causal, non-linear and time varying
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C.
non causal, non-linear and time-invariant
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D.
non causal, linear and time-variant
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Answer : Option D
Explanation :
y(t) =x(t2)
Y(t ) depends on x(t2) i.e. future values of input if t>1
Therefore the system Is non-casual
α x1(t) → y1(t) = α x1(t2 )
β x2(t) → y2(t) = β x2(t2)
Therefore α x1(t) + β x2(t) → y(t) = α x1(t2) + β x2(t2) = y1(t)+ y2(t)
Therefore the system is linear
System is time varying. Check with x(t) = u(t) “ u(t-z) → y(t) and
X1(t) = x(t “ 1) → y1(t) and find that y1(t) ≠y (t “1).
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