信号与系统信号与系统信号与系统 (2).pdf
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1、BEIJING JIAOTONG UNIVERSITYThe Course Group of Signals and Systems,Beijing Jiaotong University.P.R.CHINA.Copyright 2020Signals and Systems Deterministic signal and random signal Continuous-time signal and discrete-time signal Periodic signal and nonperiodic signal Energy signal and power signalClass
2、ification of Signals The deterministic signal is a signal about which there is no uncertainty to its value at any time.)t(x1t x tttt=()sin,R)t(x11t0tx tt t=()esin,0Ok k xkx kk k=2 sin,IDeterministic signal and random signalOtNoise signalsAudio signals The random signal is a signal about which there
3、is uncertainty before it occurs.Deterministic signal and random signalDiscussion:Are these signals in the practical applications(such as ECG signals and audio signals)are generally deterministic signals or random signals?Deterministic signal and random signal Deterministic signal and random signal C
4、ontinuous-time signal and discrete-time signal Periodic signal and nonperiodic signal Energy signal and power signalClassification of Signals The continuous-time signal is defined for all time t.It is represented as x(t),tRt is a continuous variableThere exist finite discontinuous points1102123t)t(x
5、310v011v011t)t(xContinuous-time signal and discrete-time signal The discrete-time signal is defined only at discrete instants of time.It is represented as xk,kI.k xOk k xOkk is an integer variableContinuous-time signal and discrete-time signal Relation between the C-T signals and D-T signalsSampling
6、=x kx tt kT()T0t)t(xT2T0t)t(xContinuous-time signal and discrete-time signal Deterministic signal and random signal Continuous-time signal and discrete-time signal Periodic signal and nonperiodic signal Energy signal and power signalClassification of Signals Continuous-time periodic signal x(t):if x
7、(t),a function of time,satisfies the condition+=tx tTx t for all)()(Where T is a positive constant.Clearly,if this condition is satisfied for T=T0,then it is also satisfied for T=2T0,3T0,4T0,.The smallest positive value T is termed as the fundamental period of x(t).The fundamental frequency and angu
8、lar frequency of x(t)are defined as Periodic signal and nonperiodic signal=fT1/(Hz)=fT/(rad/s)22)t(xO 0T0TtAPeriodic signal of rectangular wavePeriodic signal of triangular wave=T(s)=f/2(rad/s)2=f1/(Hz)=/(rad/s)26842862t042)t(x=T4(s)=f1/4(Hz)Periodic signal and nonperiodic signal Discrete-time perio
9、dic signal xk:if the discrete-time signal xk satisfies the condition+=kx kNx k r integer)foWhere N is a positive integer.The smallest positive integer N is termed as the fundamental period of xk.The fundamental angular frequency of xk is defined as=N/(rad)2measured in radians.Periodic signal and non
10、periodic signal k x002k2010188 k x0kDiscrete rectangular waveDiscrete triangular wave=N(rad)/0.12=N20=N10=N(rad)/0.22Periodic signal and nonperiodic signal nonperiodic signal:Any signal x(t)for which no value of T satisfies the periodic condition is termed as an aperiodic,or nonperiodic signal.Any s
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