document: Continuous-time linear systems : folklore and fact We consider a family of continuous input-output maps representing linear time-invariant systems that take a set of signals into itself . It is shown that this family contains maps whose impulse response is the zero function , but which take certain inputs into nonzero outputs . It is shown also that this family contains members whose input-output properties are not described by their frequency domain response functions , and that the maps considered need not even commute
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extractive_keyphrases: linear systems impulse response zero function frequency domain response
abstractive_keyphrases: continuous-time systems continuous input-output maps time-invariant systems commutation signal processing