Digital Signal Processing, Fall 2006

Transcription

1 Digitl Sigl Prossig, Fll 26 Ltur 5: Syst lysis Zhg-u T Dprtt of Eltroi Systs Alborg Uivrsity, Dr t@o.u. Digitl Sigl Prossig, V, Zhg-u T, 26 Cours t gl MM Disrt-ti sigls systs Syst MM2 Fourir-oi rprsttio Splig rostrutio Syst lysis MM5 Syst struturs MM6 MM4 Filtr -trsfor DFT/FFT Filtr struturs Filtr sig MM3 MM9,MM MM7 MM8 2 Digitl Sigl Prossig, V, Zhg-u T, 26

2 Syst lysis Thr ois Ti oi: ipuls rspos, ovolutio su y x h x h Frquy oi: frquy rspos Y X -trsfor: syst futio Y X LTI syst is oplt hrtri by 3 Digitl Sigl Prossig, V, Zhg-u T, 26 Prt I: Frquy rspos Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs 4 Digitl Sigl Prossig, V, Zhg-u T, 26 2

3 3 Digitl Sigl Prossig, V, Zhg-u T, 26 5 Frquy rspos Rltioship btw Fourir trsfors of iput output I polr for Mgitu gitu rspos, gi, istortio Phs phs rspos, phs shift, istortio X Y X Y X Y + Digitl Sigl Prossig, V, Zhg-u T, 26 6 Il lowpss filtr xpl Frquy rspos Frquy sltiv filtr Ipuls rspos Nousl, ot b iplt! ow to ousl syst usl? < < < π,,, < < h lp, si π,? < h

4 M ousl syst usl Csig systs Il ly h δ x Forwr iffr h δ + δ O - spl ly h δ y Bwr iffr x y h δ δ I grl, y ousl FIR syst b us by sig it with suffiitly log ly! But il lowpss filtr is IIR syst! 7 Digitl Sigl Prossig, V, Zhg-u T, 26 Phs istortio ly Il ly syst h i δ Dly istortio Il lowpss filtr with lir phs 8 i lp i, < π i, <, < < π Digitl Sigl Prossig, V, Zhg-u T, 26, si hlp, < < π Lir phs istortio Il lowpss filtr is lwys ousl! 4

5 Group ly A sur of th lirity of th phs Corig th phs istortio o rrowb sigl x s os w For this iput with sptru oly rou w, phs fft b pproxit rou w s th lir pproxitio though i rlity yb olir φ th output is pproxitly y s os φ Group ly τ gr {rg } 9 Digitl Sigl Prossig, V, Zhg-u T, 26 A xpl of group ly Figur 5., 5.2, 5.3 Digitl Sigl Prossig, V, Zhg-u T, 26 5

6 A xpl of group ly Digitl Sigl Prossig, V, Zhg-u T, 26 Prt II: Syst futios Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs 2 Digitl Sigl Prossig, V, Zhg-u T, 26 6

7 7 Digitl Sigl Prossig, V, Zhg-u T, 26 3 Syst futio of LCCDE systs Lir ostt-offiit iffr qutio -trsfor fort N M N M b b X Y M N X b Y M N x b y pol t ro t i th oitor pol t ro t i th urtor Digitl Sigl Prossig, V, Zhg-u T, 26 4 Stbility uslity Stbl h bsolutly subl hs ROC iluig th uit irl Cusl h right si squ hs ROC big outsi th outrost pol

8 8 Digitl Sigl Prossig, V, Zhg-u T, 26 5 Ivrs systs My systs hv ivrss, spilly systs with rtiol syst futios Pols bo ros vi vrs. ROC: ust hv ovrlp btw th two for th s of G. h h g G i i i δ M N i N M b b Digitl Sigl Prossig, V, Zhg-u T, 26 6 Expl So, ,.9.5 > i > u u h i

9 9 Digitl Sigl Prossig, V, Zhg-u T, 26 7 Prt III: Mgitu phs Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs Digitl Sigl Prossig, V, Zhg-u T, 26 8 Rltioship btw gitu phs I prtiulr, for systs with rtiol syst futios, thr is ostrit btw gitu phs Cosir th squr of th gitu / 2 N M N M N M b C b b 2 / /

10 A xpl P27, Expl 5. 9 Digitl Sigl Prossig, V, Zhg-u T, 26 A xpl 2 Digitl Sigl Prossig, V, Zhg-u T, 26

11 Prt VI: All-pss systs Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs 2 Digitl Sigl Prossig, V, Zhg-u T, 26 All-pss systs Cosir th followig stbl syst futio p p p ll-pss syst: for whih th frquy rspos gitu is ostt. Grl for M r M p A 22 Digitl Sigl Prossig, V, Zhg-u T, 26

12 A xpl P275 Expl 5.3, Firstorr ll-pss syst 23 Digitl Sigl Prossig, V, Zhg-u T, 26 A xpl So-orr ll-pss syst 24 Digitl Sigl Prossig, V, Zhg-u T, 26 2

13 Prt V: Miiu-phs systs Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs 25 Digitl Sigl Prossig, V, Zhg-u T, 26 Miiu-phs systs Mgitu os ot uiquly hrtri th syst Stbl usl pols isi uit irl, o rstritio o ros Zros r lso isi uit irl ivrs syst is lso stbl usl i y situtios, w ivrs systs! suh systs r ll iiu-phs systs xpltio to follow: r stbl usl hv stbl usl ivrss 26 Digitl Sigl Prossig, V, Zhg-u T, 26 3

14 Miiu-phs ll-pss opositio Ay rtiol syst futio b xprss s: i p Suppos hs o ro outsi th uit irl t /, < iiu-phs ll-pss 27 Digitl Sigl Prossig, V, Zhg-u T, 26 Frquy rspos opstio Wh th istortio syst is ot iiu-phs syst: i p i G p Frquy rspos gitu is opst Phs rspos is th phs of th ll-pss 28 Digitl Sigl Prossig, V, Zhg-u T, 26 4

15 Proprtis of iiu-phs systs Fro iiu-phs ll-pss opositio i Fro prvious figurs, th otiuous-phs urv of ll-pss syst is gtiv for π So hg fro iiu-phs to oiiuphs +ll-pss phs lwys rss th otiuous phs or irss th gtiv of th phs ll th phs-lg futio. Miiuphs is or prisly ll iiu phs-lg syst 29 Digitl Sigl Prossig, V, Zhg-u T, 26 p rg rg + rg i p Prt VI: Lir-phs systs Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs 3 Digitl Sigl Prossig, V, Zhg-u T, 26 5

16 Dsig syst with o-ro phs Syst sig sotis sirs Costt frquy rspos gitu Zro phs, wh ot possibl pt phs istortio, i prtiulr lir phs si it oly itrou ti shift Nolir phs will hg th shp of th iput sigl though hvig ostt gitu rspos 3 Digitl Sigl Prossig, V, Zhg-u T, 26 Il ly i i α, < π gr siπ α h i π α wh α h i i i α, < π α δ Il lowpss with lir phs si hlp π 32 Digitl Sigl Prossig, V, Zhg-u T, 26 6

17 Grli lir phs Lir phs filtrs Grli lir phs filtrs A A α α + β is rl futio of, α β r rl ostts 33 Digitl Sigl Prossig, V, Zhg-u T, 26 Sury Frquy rspos Syst futios Rltioship btw gitu phs All-pss systs Miiu-phs systs Lir systs with grli lir phs 34 Digitl Sigl Prossig, V, Zhg-u T, 26 7

18 Cours t gl MM Disrt-ti sigls systs Syst MM2 Fourir-oi rprsttio Splig rostrutio Syst lysis MM5 Syst strutur MM6 MM4 Filtr -trsfor DFT/FFT Filtr struturs Filtr sig MM3 MM9,MM MM7 MM8 35 Digitl Sigl Prossig, V, Zhg-u T, 26 8