Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Linear Systems: Discrete-Time Impulse Response Descriptions

  • P. J. AntsaklisEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_189-1


An important input-output description of a linear discrete-time system is its (discrete-time) impulse response (or pulse response), which is the response h(k, k 0) to a discrete impulse applied at time k 0. In time-invariant systems that are also causal and at rest at time zero, the impulse response is h(k, 0), and its z-transform is the transfer function of the system. Expressions for h(k, k 0) when the system is described by state variable equations are derived.


Linear systems Discrete-time Time-invariant Time-varying Discrete-time impulse response descriptions Pulse response descriptions Transfer function descriptions Causal At rest 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA