SME
Signals & Systems · Problem type
Pole positions: dies out, oscillates or grows
Use this for “X(s) has poles at s = −1 ± j2. Does x(t) die out, oscillate forever or grow?”
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What does the signal do as time goes on?
Tap a card, then tap its group.
Left of the jω axis (inside the unit circle for z) dies out; on it, oscillates without dying; right of it (outside the circle), grows.
Assumptions
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A pole at s = σ + jω gives a term eσt times a cosine at ω; a pole at z = p gives pⁿ.
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Each card lists every pole of the signal, and no pole is repeated.
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