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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].

2.4 c J.Fessler,May27,2004,13:10(studentversion) 2.1.2 Classication of discrete-time signals The energy of a discrete-time signal is dened as Ex 4= X1 n=1 jx[n]j2: The average power of a signal is dened as Px 4= lim N!1 1 2N +1 XN n= N jx[n]j2: If E is nite (E < 1) then x[n] is called an energy signal and P = 0. If E is innite, then P can be either nite or innite.

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