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Encyclopedia of Systems and Control pp 1–4Cite as

Linear Systems: Discrete-Time Impulse Response Descriptions

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Abstract

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.

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Bibliography

  • Antsaklis PJ, Michel AN (2006) Linear systems. Birkhauser, Boston

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  • Kailath T (1980) Linear systems. Prentice-Hall, Englewood Cliffs

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  • Rugh WJ (1996) Linear systems theory, 2nd edn. Prentice-Hall, Englewood Cliffs

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, 46556, Notre Dame, USA

    P. J. Antsaklis

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  1. P. J. Antsaklis
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Correspondence to P. J. Antsaklis .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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© 2014 Springer-Verlag London

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Antsaklis, P.J. (2014). Linear Systems: Discrete-Time Impulse Response Descriptions. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_189-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_189-1

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  • Publisher Name: Springer, London

  • Online ISBN: 978-1-4471-5102-9

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

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