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1、Ch 7 SamplingSamplingSome values or samples are extracted from a signal,at points equally spaced in time.Importance A continuous-time signal nn discrete-time signalDiscrete-time signals are preferable to transmitting,processing,inexpensive,lightweight,programmable,easily reproducibleTwo channelsOne
2、channel7.1 Representation of a continuous-time signals by its sampling Sampling needs condition)(),(),(321txtxtx)(1kTx)(2kTx)(2kTx7.1.1 Impulse-train samplingNnTttp)()(nnTttxtptx)()()()(nnTtnTx)()()(txp)()()(tptxtxp)()(*)(21jXjPjXpkNTkTnTttp)2(2)()(F)2(*)(1)(kpTkjXTjX)2(1kTkXTMMsT ,2s Note,Reconstru
3、ction:)()()(jXjHjXpr In frequency domain,0 ,)(ccTjHSampling Theorem.cos)(if11ttx withsignal limited-band a be)(Let tx.Mfor0)(jXuniquely is)(Then tx,)(samples itsby determinednTx,.,2,1,0n,2 ifMs./2 whereTs s Niquiste,奈奎斯特频率（奈奎斯特频率（MM）Ex.);(*)()(211txtxtyThe maximum frequency of x1(t),x2(t)are 50Hz,15
4、0Hz,respectively.determinate the minimum sampling frequency of following signals：),()()(212txtxtydXXY)()()(2127.1.2.Sampling with a Zero-order Hold(零阶保持采样零阶保持采样)TttTtth ,0 ,00 ,1)(0 Zero-order Hold Sampling：A system samples x(t)at a given instant and holds that value until the next instant at which
5、a sample is taken.nnTthnTx)()(0nthnTtnTx)(*)()(0)(*)()(00txthtxpnnTtnTxth)()(*)(0Reconstruction of a signal of the Zero-Order Hold),()(*)(0jHththlpr)2/sin(2 TF)2/sin(2 2/TeTjF)()()()(*)(00jHjHjHththlprrF)2/sin(2)()(2/TjHejHlpTjr7.2 Reconstruction interpolation in time domain Different kinds of inter
6、polationZero-order hold with horizontal linefirst-order hold linear interpolation(with straight line)Band-limited interpolation using ideal lowpass filterInterpolation a set of sample valuesgg fit of a continuous signal Band limited interpolation),(*)()(thtxtxpr)(*)()(thnTtnTxn)(*)()(thnTtnTxnnnTthn
7、Tx)()(ttTthccc)sin()(nrnTxtx)()(So内插内插函数函数)()(sin(nTtnTtTcccZero-order Hold InterpolationTttTtth ,0 ,00 ,1)(0nnTthnTx)()(0)(*)()(00txthtxp Examples for the applications of zero-order fold interpolation(a)脉冲抽样脉冲抽样(b)零级保持零级保持-重建重建(c)图图(a)的的1/4间隔抽样，间隔抽样，零级保持零级保持-重建重建 First-order fold interpolationnnTth
8、nTx)()(1)(*)()(11thtxtxp2 12/)2/sin(1)(TTjHTTtth|t|,|1)(1nnTtnTxth)()(*)(17.3 The effect of under-sampling:aliasing,2Msttx0cos)(Let NnTttp)()()(*)()(21jPjXjXp)()(00kTkT)2(2FkskjXT)(1,6 )1(0s0)2/6()2(s0)4/6()3(s0)5/6()4(s)()()(ssjXjXjX2/00s5/00sEx.7.1 Suppose x(t)is sampled at sampling frequency s,de
9、terminate the resulting output of the following system.)sin(2sin)cos(2cos)(tttxss)(txnspnTtnTtx)()cos(2cos)(Solution:sT2)cos(2cos)(ttxsrMs2 theoremSampling Particular usage of the aliasingSampling oscilloscope 采样示波器采样示波器:频闪测速频闪测速:旋转圆盘旋转圆盘频闪器频闪器0s7.4 Discrete-time processing of continuous-time signal
10、s模拟数字转换模拟数字转换数字模拟转换数字模拟转换 x d n=x c(n T)中的时域关系中的时域关系nnjcjdenxeX)()(nTxnxcdncdnknxkx将将x c(n T)视为离散时间信号视为离散时间信号x c n涉及了频域尺度变换。涉及了频域尺度变换。)/(|)(/)(TjXeXTpnxnTxjdncpnTtnTxtx)()()(nnTjcpenTxjX)()()2(1)(kpTkXTjX)2/(1)(kcjdkTjXTeX x d n=x c(n T)中中的频域关系的频域关系F 不同采样率的时不同采样率的时/频域关系频域关系，例，M，sT5.014/2Ts)/)2(1)(kc
11、jdTkjXTeXkckjXT)2(2(1)4(1)(kpkXTjX)2(1)(kpkXTjX：，21sT)2(1)(kcjdkjXTeX Discrete-time processing of continuous-time signalsSummary1.Method of changing continuous-time signals into discrete-time signals.2.Condition of reconstruction signals3.Method of reconstructing signals4.Basic problem determine the max of signals which are changed or calculated.
信号与系统资料：Ch7 Sampling
