= Formal sinusoidal response of an unstable linear system
Substitution $s=i\omega$ into an algebraic <transfer function> can produce finite amplitude and <phase> even when the causal system has unstable <poles>. It then describes a sinusoidal particular solution whose growing homogeneous response is not generically absent. A physically settled <frequency> response requires transient <asymptotic stability>; for an unstable causal <transfer function>, its Laplace region of convergence need not include the imaginary axis.
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