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Signals and Systems

In: Discrete-Time Linear Systems

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  • Guoxiang Gu

    (Louisiana State University, Department of Electrical and Computer Engineering)

Abstract

Mathematical models are indispensable in design of both communication and control systems. Although signals and systems in feedback control are in continuous-time, and digital communications are in discrete-time, the wise use of digital computers in control systems and the emergence of wireless Internet have diminished the difference between feedback control and data communications. Both are now in discrete-time and both are MIMO systems. More importantly they tend to use increasingly the same mathematical descriptions in modeling and share more and more mathematical tools in design. This chapter presents various linear models for discrete-time signals and systems. It begins with deterministic and energy bounded signals, and then covers the random processes with bounded mean power. Vector signals and their associated spectral densities are introduced to facilitate the analysis. Different dynamic models are presented to describe the linear MIMO systems, including transfer matrices and state-space systems. Linear time-varying systems are also studied in this chapter. Finally optimal symbol detection is analyzed for the binary case, and bit-error rate in digital communication is introduced and analyzed.

Suggested Citation

  • Guoxiang Gu, 2012. "Signals and Systems," Springer Books, in: Discrete-Time Linear Systems, edition 127, chapter 0, pages 31-66, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-2281-5_2
    DOI: 10.1007/978-1-4614-2281-5_2
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