Fundamental Concepts ppt课件


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Fundamental Concepts ppt课件内容预览:§1-2 Discrete-TimeSignals§1-3 Discrete-timeSystems§1-4 Basic Properties of Discrete-timeSystemsProblems§1-1IntroductionThe concepts of signals and systems arise in virtually all areas of technology,ranging from appliances or devices found in homes to very sophisticated engineering innovations. In fact,it can be argued that much of the development of high technology is a result of advancements in the theory and techniques of signals and systems.Last term,in the course of signals and systems,we have studied the continuous-time system analysis. In this term,we are going to study the discrete-time system analysis. Let us begin with the fundamental concepts of the discrete-time system analysis.§1-2 Discrete-TimeSignalsDefinitions:Discrete-time variable: The time variable t is said to be a discrete time variable if t takes on only the discrete values t=tn for some range of integer values of n.Discrete-time signals: A discrete-time signal is a signal that is a function of the discrete time variable tn,denoted with x(tn),where x(t)is a continuous-time signal.The resulting discrete-time signal x(tn)is called the sampled version of the original continuous-time signal x(t).Let tn=nT,where T is called the sampling interval. If T is a constant,the sampling process is called uniform sampling,otherwise,nonuniform sampling. Note that the nonuniform sampling is sometimes used in applications but is not considered in this course. So,we often use x[n]to denote x(tn),i.e.,x[n]=x(tn)=x(t)|t=nT=x(nT)Also note that the square brackets instead of parentheses are used to denote the discrete-time signal x[n].For example,pptwhere T=115,n=0,1,2,…,30. The plots of x[n]and x(t)are given in Fig.1-1Fig.1-1Typical and Simple Examples of Discrete-TimeSignalsDiscrete-time Unit-step Function u[n]Definition:The plot of u[n]is shown in Fig.1-2Fig.1-2Discrete-time Unit-ramp Function r[n]Definition:The plot of r[n]is shown in Fig.1-3Fig.1-3UnitPulseDefinition:The plot of δ[n]is shown in Fig.1-4Fig.1-4Periodic Discrete-timeSignalsDefinition: A discrete-time signal x[n]is periodic if there exists a positive integer r such thatx[n+r]=x[n]for all integers nHence x[n]is periodic if and only if there is a positive integer such that x[n]repeats itself every r time instants,where r is called the period.The fundamental period is the smallest value of r for which the signal repeats.For example,let us examine the periodicity of a discrete-time sinusoid given byx[n]=Acos(Ωn+θ)The signal is periodic ifAcos[Ω(n+r)+θ]=Acos(Ωn+θ)Recall that the cosine function repeats every 2πradians,so thatAcos(Ωn+θ)=Acos(Ωn+2πq+θ)For all integers q. Therefore,the signal Acos(Ωn+θ)is periodic if and only if there exists a positive integer r such that Ωr=2πq for some integer q,or equivalently,that the discrete-time frequency Ωis such that Ω=2πqr for some positive integers q and r.The discrete-time sinusoid x[n]=Acos(Ωn+θ)is plotted in Fig.1-5.For the case when Ω=π3and θ=0,which is plotted in Fig.1-5(a),the corresponding period is found to be r=2πqΩ=6q and the fundamental period is 6.
课件关键字:Fundamental Concepts ,Fundamen。

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