离散时间信号与系统--复习.ppt

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1、1,Discrete-Time Signals and Systems离散时间信号与系统,2,Discrete-Time Signals: Sequences,Discrete-time signals are represented by sequence of numbers The nth number in the sequence is represented with xn Often times sequences are obtained by sampling of continuous-time signals In this case xn is value of the

2、 analog signal at xc(nT) Where T is the sampling period,3,Representation of Sampling,Mathematically convenient to represent in two stages Impulse train modulator Conversion of impulse train to a sequence,Convert impulse train to discrete-time sequence,xc(t),xn=xc(nT),x,s(t),-3T,-2T,2T,3T,4T,-T,T,0,s

3、(t),xc(t),t,xn,-3,-2,2,3,4,-1,1,0,n,4,Basic Sequences and Operations,Delaying (Shifting) a sequence Unit sample (impulse) sequence Unit step sequence Exponential sequences,5,Sinusoidal Sequences,Important class of sequences An exponential sequence with complex xn is a sum of weighted sinusoids Diffe

4、rent from continuous-time, discrete-time sinusoids Have ambiguity of 2k in frequency Are not necessary periodic with 2/o,6,Discrete-Time Systems,Discrete-Time System is a mathematical operation that maps a given input sequence xn into an output sequence yn Example Discrete-Time Systems Moving (Runni

5、ng) Average Maximum Ideal Delay System,T.,xn,yn,7,Linear Systems,Linear System: A system is linear if and only if Examples Ideal Delay System,8,Time-Invariant Systems,Time-Invariant (shift-invariant) Systems A time shift at the input causes corresponding time-shift at output Example Square Counter E

6、xample Compressor System压缩机系统,9,Causal System,Causality A system is causal its output is a function of only the current and previous samples Examples Backward Difference反向差分 Counter Example Forward Difference正向差分,10,Stable System,Stability (in the sense of bounded-input bounded-output BIBO) A system is stable if and only if every bounded input produces a bounded output Example Square Counter Example Log,