M7. Introduction to Sampling of Continuous-Time Signals

Transcription

1 M7. Iroduio o Samplig of Coiuou-im Sigal Radig marial: p /22/2011 I. Dir-im Sigal ad Sym 1

2 Co Wha h amplig mhaim? Wha h aliaig problm? Nyqui amplig horm Frquy aalyi of amplig 3/22/2011 I. Dir-im Sigal ad Sym 2

3 Iroduio Dir-im igal a b ommoly obaid by amplig h oiuou-im igal Digial ompur a oly dal wih digial igal, whih i a pial la of dir-im igal Digial igal proig, digial orol ym oruio Sigal proig Samplig ad holdig D/A Compur A/D ipu Ipu oi Pla oupu Oupu diurba 3/22/2011 I. Dir-im Sigal ad Sym 3

4 Priodi Samplig A qu of ampl [], a oiuou-im igal [], - < < Samplig priod, amplig frquy f1/ Hrz; or amplig frquy 2π/ rad/ Praially, h opraio of amplig i implmd by aalog-o-digial A/D ovrr Quaizaio of h ampld oupu Liariy of quaizaio p Sampl-ad-hold irui Limiaio o h amplig ra Priipl of amplig Graig a impul rai from h oiuou-im igal Covrig h impul rai o a dir-im qu 3/22/2011 I. Dir-im Sigal ad Sym 4

5 Priipl of Samplig 3/22/2011 I. Dir-im Sigal ad Sym 5

6 Frquy Aalyi of Samplig Graio of a impul rai hrough modulaio of h uiformd priodi impul rai σ σ σ h Fourir raform of a priodi impul rai i a priodi impul rai i frquy domai S 2 π 2 π σ, 3/22/2011 I. Dir-im Sigal ad Sym 6

7 3/22/2011 I. Dir-im Sigal ad Sym 7 Frquy Aalyi of Samplig Co d h frquy-domai rlaio bw ad oi of priodially rpad opi of!!! ould b rovrd poibly from wih a idal lowpa filr if σ σ S π σ π 2, 2 S 1 * 2 1 π

8 Eff of Samplig i Frquy Domai Coidr a badlimid igal wih high ozro frquy N If >2 N, hr i o ovrlap wih rplia of, o, ould b rovrd poibly from If <2 N, hr i ovrlap wih rplia of, h, Aliaig diorio aliaig Ei i h rovrd igal hrough 3/22/2011 I. Dir-im Sigal ad Sym 8

9 Ea Rovry from Samplig Coidr badlimid igal Udr odiio >2 N U a idal lowpa filr H r wih gai ad uoff frquy uh ha N < < - N h oiuou igal a b aly rovrd a r 3/22/2011 I. Dir-im Sigal ad Sym 9

10 Alia ad Nyqui Samplig horm If <2 N, aliaig phomo our Coidr a oi igal o 0 Nyqui Samplig horm L b a badlimid igal wih r 0 for > N, h i uiquly drmid by i ampl [], - < <, if 2π/ 2 N 3/22/2011 I. Dir-im Sigal ad Sym 10

11 3/22/2011 I. Dir-im Sigal ad Sym 11 Rlaio bw ad i h oiuou Fourir raform of i h dir Fourir raform of [] h Fourir raform of impul rai fuio h hr i i.., a frquy alig or ormalizaio d wk k k ] [ σ π

12 Eampl: Samplig ad Aliaig Eampl 4.1 p.147 amplig ad roruio Eampl 4.2, 4.3 p Aliaig i roruio! Should b π/ 3/22/2011 I. Dir-im Sigal ad Sym 12

13 Roruio of Badlimid Sampld Sigal Priipl of roruio Graig a impul rai from dir-im qu [ ] σ Covrig h impul rai o a oiuou-im igal r [ ] π i π / / Roruio lowpa filr i π / h r π / [ ] h r r 3/22/2011 I. Dir-im Sigal ad Sym 13

14 3/22/2011 I. Dir-im Sigal ad Sym 14 Dir-im Proig of Coiuou-im Sigal C/D ovrr produ a dir-im qu D/C ovrr ra a oiuou-im igal LI dir-im ym h ovrall ym i quival o a LI oiuou-im ym 2 1, ] [ π < ohrwi Y Y H Y y y r r r 0, /,, / / i ] [ π π π ], [ ]* [ ] [ H Y h y < H H H Y ff ff r / 0, /,, π π

15 Eampl of Dir Proig Eampl 4.4 p.155 LI dir-im ym: a idal lowpa filr Badlimid ipu igal Samplig ra aifi Nyqui horm h ffiv ym i a LI oiuou-im ym wih h ffiv uoff frquy / 3/22/2011 I. Dir-im Sigal ad Sym 15

16 Praial Iu i Implmaio I prai, Coiuou-im igal ar o prily badlimid Idal lowpa filr a o b ralizd Idal C/D ad D/C ovrr a oly b approimad by dvi alld A/D ad D/A ovrr hrfor, Prfilrig o avoid aliaig A/D ovrio: ampl ad hold irui, quaizaio D/A ovrio. 3/22/2011 I. Dir-im Sigal ad Sym 16

17 Eri Sv Problm 4.4 o pag214 of h book; Problm 4.5 o pag214 of h book; 3/22/2011 I. Dir-im Sigal ad Sym 17

18 Cour Summary M1. Dir-im Sigal ad Sym M2. h Z-raform ad i Propri M3. h Ivr Z-raform ad Frquy- Domai Rpraio M4. Fourir raform ad I Propri M5. LI Sym Dribd by Liar Coa Coffii Diffr Equaio M6. Frquy Rpo of LI Sym M7. Iroduio o Samplig of Coiuou-im Sigal 3/22/2011 I. Dir-im Sigal ad Sym 18