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Discrete-time signals and systems

Chapter2 discrete -timesignalsandsystemsContentsOv erview.. cationofdiscrete-timesignals.. cationofdiscrete-timesystems.. Amplitude properties.. :theconvolutionsum.. andnonrecursive discrete -timesystems.. cientdifferenceequations.. cientdifferenceequations.. LTIrecursive system.. andnonrecursive realizationofFIRsystems.. J. Fessler, May27,2004,13:10(studentversion)Overview terminology, classesofsignalsandsystems,linearity,tim e-invariance. impulseresponse,convolution,differenceeq uations,correlation, :eventuallyDSPsystemdesign;must rstlearntoanalyze! :single-channel,continuous-valuedsignals ,namely1 Ddiscrete-timesignalsx[n].Inmathematical notationwewritex:Z!Rorx:Z!C x[n]canberepresentedgraphicallyby stem plot. x[n]isnotde nedfornonintegern. (Itis not zero despiteappearanceofstemplot.) We callx[n] willalsoconsider2 Ddiscrete-spaceimagesx[n; m].

unit sample sequence or unit impulse or Kronecker delta function (much simpler than the Dirac impulse) ... = u[n] u[n 1]. This is the discrete-time analog of the continuous-time property of Dirac impulses: (t) = d dtu(t). exponential signal or geometric progression (discrete-time analog of continuous-time eat) x[n] = an plotfor0 < a < 1 real ...

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