Properties of Time-Variant Convolution

  • Joachim SpeidelEmail author
Part of the Signals and Communication Technology book series (SCT)


It is interesting to check whether the time-variant convolution encompasses the time-invariant convolution. By definition, the impulse response h(t) of a time-invariant system is the response to an input Dirac impulse \(\delta (t).\) If the system is excited by the time-shifted Dirac impulse \(\delta (t-s)\), the response \(h(t-s)\) also incorporates a shift without changing its original shape.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of TelecommunicationsUniversity of StuttgartStuttgart, Baden-WurttembergGermany

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