Muliae Signal Pocessing Chape 7 D. Badley J. Bauin Wesen Michigan Univesiy College of Engineeing and Applied Sciences Depaen of Elecical and Copue Engineeing 93 W. Michigan Ave. Kalaaoo MI, 498-5329
Chape 7: Resapling Files 7. Inepolaos 54 7.. Siple -o-m Inepolao 54 7.2 Inepolao Achiecue 6 7.2. Polyphase Paiion 6 7.3 Band-pass Inepolao 64 7.4 Raional Raio Resapling 69 7.5 Abiay Resapling Raio 7 7.5. Neaes Neighbo Inepolaion 72 7.5.2 Two Neighbo Inepolaion 8 7.6 Faow File 85 7.6. Classical Inepolao 85 7.6.2 Polynoial Appoxiaion 89 7.6.3 Faow File 92 2
Inepolaion Concep :4 Shaping Pio o inepolaion pocessing. 3
Inepolaion-File If you ae going o inepolae, Inepolae o a sufficien ae o iniie follow-on file concens, paiculaly when a digial o analog convee (DAC) is involved. The digial file can (should) be based on he oiginal signal passband and whee he eplicas will occu. Exaple: fsop = oiginal fs-fpass ay wok Alenaely: fsop = oiginal fs-(fpass+fsop)/2 ay wok Mos Consevaive: fsop = fs/2 4
Inepolao - Desied Fileing Pos-inepolaion file o eliinae eplicaed coponens File Specificaion 5
Inepolaed Replicas and File File Design: NN=fipod([.75 3.25],[ ],[..],28) The esponse o his call is: NN = 3, use 28 ap as sufficien 6
Coposie and Resuling Responses Above: eplicaed bands and he file o be applied Below: Pos-fileing signal specu 7
Zoo o Naowband Resul Above: eplicaed bands and he file o be applied Below: Pos-fileing signal specu 8
An Alenae File: Don Cae Bands We only cae abou aenuaion wee he eplicas exis! Theefoe, why ove-consain he FIR file and fip? 9
Coposie and Resuling Responses Above: eplicaed bands and he file o be applied Below: Pos-fileing signal specu
Zoo o Naowband Resul Above: eplicaed bands and he file o be applied Below: Pos-fileing signal specu
Copaison Above: Oiginal File Below: Don Cae Band File 2
Copaison - Naowband Above: Oiginal File Below: Don Cae Band File 3
File Coefficiens Above: Oiginal File Below: Don Cae Band File 4
Making he file wok. Adjus he passband weigh fo fip. A equal weighs he passband ipple is oo sall Reduce he passband weigh o 2/M fo bee esuls 2. Naow he eo egion aound he specal eplicas Use Nyquis passband wih oll-off. The cobined effec of he oll-off and file povide sufficien aenuaion This also widens he s ansiion fo he passband o sopband. 5
MATAB Siulaion See chap7_. Sae as given in ex book and slides See chap7_a. Tweaked (inceased naps) o ee sop-band aenuaions See chap7_b. Don Cae egula and yff See chap7_c. ASK odulaed es signal (4 saples pe sybol, nyquis file) 6
Inepolao Achiecue x M wn hn yn Basic Inepolao Inepolao wih Coplex Fequency Mixing x M wn hn y nk W M 7
Invese Achiecues We can inve he file deciaion pocess. In geneal, whaeve achiecue flows in one diecion, an invese ha flows in he exac opposie diecion is possible! 8
Channelie Selec one of M specal bins in an FDM specu. 9
Figue 6.3 Speca Up/Down Convesion Speca Obseved A Vaious Poins in Pocessing Chain of Sandad Down Convee Upconvee opeaes fo boo o op! 2
2 Z-Tansfo Inepolaion File Mah A siila sucue in M as seen befoe Theefoe we can use a polyphase sucue o pefo fileing as follows N n n n h M M N M M h M N M M M h M N M M
Inepolaion Polyphase Sucue N M M M Z Z The noble ideniy can be applied 22
Pos Polyphase Inepolaion Noice ha he delay eleens idenify a couao 23
Polyphase Inepolao The invese sucue fo he file-deciao 24
25 Bandpass Inepolaos Incopoae oupu ixing (x o he h Nyquis Band) Use Bandpass files insead of owpass files 2 exp k k n x k h n i n y e k s n 2 exp s x h s i s y n h x w n n y nk W
26 Bandpass Inepolaion (2) This fo uses a coplex file on he eplicaed speca 2 exp s x h i s y 2 exp s x h i s y 2 exp s x h i s y 2 exp s x i h s y This fo uses a coplex pe-uliplicaion fo each polyphase pah
Coplex Shif h File Equivalence h x yn h 2 nk W M h k W M h M x h k W M yn h 2 k W 2 M h M M k W M 27
Coplex Shif (2) k W M h y s h exp i 2 x s x k W M h yn k W 2 M h 2 A vesion wih eal fileing of coplex coefficiens The inpu is oupu in he Nyquis one defined by k. Quesion: is hee a sucue whee we could fill all he bands siulaneously? M k W M h M 28
29 X daa povided fo evey band One Bandpass band Su of all bandpass bands 2 exp s x i h s y 2 exp s x i h s y 2 exp s x i h s y Fileing he (-s) veco oupus of an M-poin IFFT
A Tans-uliplexe This sucue geneaes a fequency-division-uliplexed oupu fo he M discee naowband inpus! Exensively used in ealy elephony fo analog FDM x h y s h exp i 2 x s x x 2 FFT h h 2 yn x M h M 3
MATAB Siulaion See Chap7_inepfilev. FFT based inepolaion See Chap7_inepfilev2. IFFT based inepolaion 3
FDM Geneaion and Pocessing Foing Wideband and Refoing Naowband Files naowe han he Nyquis egions ae used fo geneaing FDM wavefos. A guad band beween adjacen fequencies is ypically used x h h y x h h y yn xn x 2 FFT h 2 h 2 IFFT y 2 x M h M h M y M Synhesis OFDM Sybol Basis Analysis 32
Quadaue Mio File Pocessing Obseving Naowband and Refoing Wideband Significan file esicion ae equied if he oupu is equied o appoxiae he inpu! Quadaue Mio File Definiion and Requieens h y x h h y x h xn yn h 2 IFFT y 2 x 2 FFT h 2 h M y M x M h M Analysis Synhesis 33
QMF Equaions Analysis Synhesis (subsiue and =M) xˆ y k M exp j2 h x s M h exp i 2 y s M k M Invese aheaical pocesses M IFFT wih invese FFT Boadband o naowband and back o boadband Files ae ciical fo oveall pefoance. 34
QMF Applicaions Fequency doain fileing o equaliaion Tie-Specal Analysis wih econsucion Abiaily ake signals apa and hen econsuc he Paial-Band Synhesis o one o oe abiay bandwidhs (univesal base saion eceive) Paial-Band Analysis wih fequency doain suaion and fullband synhesis (univesal base saion ansie) Applicaions: cellula elephone base saions, saellie elay saions, ec. 35
Quadaue Mio Files Achiecually, he sucue is ioed acoss he cenal axis in es of he analysis and synhesis pocessing Pefec Reconsucion of he inpu signal is desied, bu Quasi-Pefec is usually accoplished ook fo PR-QMF o Quasi-PR QMF The QMF opeaion is ypically descibed in es of wo files Z 2 w n 2 Z xn Z 2 w n 2 Z xˆ n 36
37 2-Bank QMF Pefec Reconsucion Condiions Z n x 2 n w n xˆ Z 2 n w 2 2 Z Z X X X 2 2 ˆ X X X 2 2 ˆ X X 2 ˆ
2-Bank QMF Pefec Reconsucion Condiions Xˆ X T 2 w w w 2 Addiional Condiions (opiiaion) 2 w, fo w w w, fo w Passband 2 38
Pojec Assignen Discussion. Find a pape descibing he ipleenaion of a file ha can be used in a Quadaue Mio File ook in IEEE Tansacions on Cicuis and Syses II: Analog and Digial Signal Pocessing D. Bauin us appove of all papes/files seleced. 2. Ipleen he file using MATAB Povide a funcion ha geneaes he file coefficiens based on a desied se of inpu cieia (i.e. filecoef=nae(inpupaaees)) Veify ha you have geneaed he coec file coefficiens by copaing he o values o cuves povided in he pape. 3. Use he QMF analysis-synhesis MATAB scip ha will be developed o povided in class o chaaceie he esuls of you file. Pos-analysis file ipple, bandwidh, sopbands, ec. Pos-synhesis inpu o oupu eo, eo fequency esponse, ec. 39
Raional Rae Resapling Wha happens if we wan an oupu ae ha is P/Q whee P and Q ae ineges. File-deciae and hen inepolae-file, o Inepolae-file and hen file deciae h Q n Q P y h P xn P h P k h Q k Q y Which one can use fewe files? Inepolae-deciae 4
Raional Rae File The file is defined based on he lage of P o Q If P is geae, he baseband Nyquis Zone us be isolaed fo he ohes pio o deciaion If Q is geae, he file ha eliinaes aliasing when deciaion is pefoed is naowe han he baseband Nyquis Zone. 4
Raional Rae File Ipleenaion Ipleenaion Build a polyphase file sucue fo inepolaion, bu hen only ake evey Qh oupu fo he couao as shown in Fig. 7.2 42
Abiay Resapling Raio In he pevious exaple, he inepolaos oupu couao was sapled a fixed inevals accoding o he inege denoinao of P/Q Wha would happen if Q wee non-inege and we seleced he couao oupu ie saple closes o he one desied? O inepolae beween wo saples? 43
Abiay Raio Resapling Inepolaion Neaes Neighbo 44
Pefoance Exaple (sae aio) o 5 Inepolaion: 5/ 32/6.4 Inepolae-Deciae Sopband sidelobes inceased 45
Pefoance Exaple (2) 32/6.4 Inepolae-Deciae 32/6.37 Inepolae-Deciae Sopband sidelobes wose 46
Malab Exaple Chap7_2. Raional Rae Exaple wih ineges: 4/7 ae. Chap7_3. Raional Rae Exaple wih non-ineges: 32/6.37 ae. Neaes neighbo oupu saple 47