SME
Signals & Systems · Problem type
Linear and time-invariant systems
Use this for “Is the system y(t) = t·x(t) linear? Is it time-invariant?”
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Linear: scaled and added inputs give scaled and added outputs. Time-invariant: a delayed input gives the same output, delayed.
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Assumptions
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Linear: scaled and added inputs give scaled and added outputs, so a zero input gives zero output.
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Time-invariant: a delayed input gives the same output, delayed; nothing in the rule reads the clock t itself.
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Each system in the last bin is linear; it fails only time-invariance.
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