上海交大dsp課程ppt第四章(精)

1、Chapter 4 sampling ofcontinous-time signals4.1 periodic sampling4.2 discrete-time processing of continuous-time signals4.3 continuous-time processing of discrete-time signal4.4 digital processing of analog signals4.5 changing the sampling rate using discrete-time processing4.1 periodic sampling1.ide

2、al sample4W=T（Q rui=T（uL）T：sampleperiodfs=l/T:samplerateQs=27t/T:samplerate-4 -3-2-101234_4 _3 2 1 0 I 234Figure 4.1 ideal continous-time-to-discrete-time(C/D)converterFigure 4.2(a) mathematic node for ideal C/Dxn - xc(nT)Figure 4.3s2TT禮訂nZ)f-20,-a4ft.m,d nA A A皿-a -nv/ A. X Xn.20sg n忌 3 an4/vvx/v/

3、11 X A aliasing frequency艮晉也nJ 2”J LCO = Q1aliasingX（e）=Xs（jC）lde/yI s=-Nxc（J（3 k2巧IT）k=-sfrequency spectrumchange of ideal sampleXXc（J（G_RGs）k=sNo aliasingPeriod =27iin time domain：w=2.17tand w=0.17tare the sametrigonometric function property82（y冋）=coz（03）high frequency is changed into low frequenc

4、y in time domain：w=l 1兀and w=0.9zare the same2.ideal reconstructionFigure 4.10(b) ideal D/C converterideal reconstruction in frequency domainFigure 4.4ilyvVV (C.Y C,V) )EXAMPLEFigure 4.5A”1-OoTHoan7T仏!- a -n0Tn0QvT xg)2 nn77Q,0o7=TAL !fflt-uT心QTake sinusoidal signal for example tounderstand aliasing

5、 from frequency domain、7No aliasing扎（川）Li1r*山nAliasingx,（川）rL11-(Qs-do)QEXAMPLExa(r) = cos(2*5f),0t l.f = 5HzSampling frequency:8HzReconstruct frequency：廣=8 5 = 3HZIdeal reconstruction svsteni-1Figure 4.10(a) mathematic model for ideal D/Cxg) =x $ g)H3)十 g)TIQ lXg) =X$g)H(j hr(t)=IFTHr(j) = 4-r Hg)e

6、G dG斗W dG2n J-2n丿譏sin( Qj) sin(r/T)ntlT ntIT:.xr(t) = xs(t)*hr(t) = xnS(t-nT)*-xj八7 /ff一 iIm、1彳LXt JFigure 4.90 t(C)3.Nyquist samplingtheoremsNyquist sampling theorems:let xc(t) be a bandlim ited signal withXC(JQ) = OJQIQATthen xc(t) is uniquely det er min ed by its samples xn = xc(nT)9n = 0,l,2,if

7、Qv- Qy OlN,that is0S =耳)N2GN、or (A = y)2/NG、/2: nyquist frequency2G“ : nyquist rateQs2QN:oversamplingG、 2Qv: undersampling-Oc.ncnQr= Q/2TFigure 4.41 Digital processing of analog signalsexamples of sampling theorem (1 )The highest frequency of analog signal ,which wav file with sampling rate 16kHz ca

8、n show ,is：8kHzThe higher sampling rate of audio files, the better fidel讓y.數(shù)字電話中的音頻館號W-OAV-zCD中的音頻信號?$-COexamples of sampling theorem(2)according to what you know about the sampling rate of MP3 file, judgethe sound we can fee)frequency range( B )Matlab codes to realizeinterpolationxa(r) =COS(IOM)J)t

9、 .f = 5Hz f =io/z(r = o.i5)$draw xn = xa(nT) = cos(K)r)= cos(加7)drawreconstruction signal:co,y(0 =工xnn二sswn(t-nT)ITn(t-nT)/T(A) 2044kHz(B) 2020kHzEXAMPT=O.I; n=0:10;dt=0.001; y=x*sinc(卜n*T)/T): x=cos( 1O*pi*n*T);t=ones( 11,1)* O:dt:ll;hold on;stem(n,x)；n=n*ones( 1/dt+1);plot(t/T,y；r,)Supplement: ban

10、d-pass sampling theorem：=2(幾-九)(1 + M/N) N = int .5、/H-九丿M=f-.J- .-N/H- /L)/H=5B心2幾fs= 2fH/N = 2BW= 2B丫)= 2(1 + M /N)4.1 summary1 .representation in time domain of sampling=T()血)2.changes in frequency domain caused by samplingXV(JQ) = - 22xc(J(Q-Z;Qv)X(eJa)=- 2XcU(eo-k2rr)/T)g-S)廣 d3understand rec o

11、n struction in freque ncy domain(c)z.on)廠v q.v4. understand reconstruction in time domain/f t一、ir-t丁(e)5. sampling theoremRequirements and difficulties：frequency spectrum chart of sampling and reconstructioncomprehension and application of sampling theoremh)Figure 4.124.2 discrete-time processing of

12、 continuous-time signalsQ7r/Tconditions： LTI； no aliasing or aliasing occurred outside the pass band of filtersEXAMPLEFigure 4.11EXAMPLEaliasing occurred outside thepass band of digital filterssatisfies the equivalentrelation of frequencyresponse mentioned before. )Figure 4.13叫(UIW _匕十/_ ! /亦廠 f寧 4.3 continuous-time processing of discrete-time signalhn(P/E)Figure 4.16FZ：2FUAZT)2rr-嶂 -芋-爭導(dǎo)蘆gv(K)Figure 4.12EXAMPLEIdeal delay system： noninteger delayH(eJa) = Hc(jco/T)far coorecord the digital soundZlcro-ordcrTkiciil inturxlaling filter7TTholdFigure 4.5Influence caused by sampling ratea