Transcription of Lecture III: Systems and their properties
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Lecture III: Systems and their properties
Lecture III: Systems and their propertiesMaxim RaginskyBME 171: Signals and SystemsDuke UniversitySeptember 3, 2008 Maxim RaginskyLecture III: Systems and their propertiesThis lecturePlan for the Lecture :1 What is a system ?2 system properties :causalitymemorylinearitytime invariance3 linear time-invariant (LTI) systems4 Nonlinear systemsMaxim RaginskyLecture III: Systems and their propertiesWhat is a system ?Recap:a system is any physical device, process or computer algorithmthat transforms input signals into output :electronic circuitsbiological Systems : audiovisual system , cardiovascular system , Systems : the stock market, social networks, processors in scientific or medical equipment or inaudio/video devicesWe will state our definitions for continuous-time Systems . They areessentially the same for discrete-time RaginskyLecture III: Systems and their propertiesCausalityA systemSiscausalif the output at timetdoes not depend on thevalues of the input at any timet > predictor:y(t) =x(t+ 1) noncausal since the output attimetdepends on the input at future timet+ 12 Ideal delay:y(t) =x(t 1) causal since the output at timetdepends only on the input at past timet 13 Moving average (MA) filter:y[n] =x[n 1]+x[n]+x[n+1]3 notcausal, since the output at timendepends in part on the input atfuture timen+ 1 Most physical Systems are causal.
Systems that are not time-invariant are called time-varying. Classic example: systems described by linear differential equations with constant coefficients, such as 5 d2y(t) dt2 − 3y(t) = − dx(t) dt +2x(t). Linear (RLC) circuits are described in this way. Maxim Raginsky Lecture III: Systems and their properties
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