ELEG- Sigal Procssig ad Commuicatios Lctur Frqucy Rspos of FIR Filtrs READING ASSIGNENTS This Lctur: Chaptr 6, Sctios 6-, 6-, 6-3, 6-4, & 6-5 Othr Radig: Rcitatio: Chaptr 6 FREQUENCY RESPONSE EXAPLES Nxt Lctur: Chap. 6, Scts. 6-6, 6-7 & 6-8 ECE- Sigal Procssig First LECTURE OBJECTIVES SINUSOIDAL INPUT SIGNAL DETERINE th FIR FILTER OUTPUT FREQUENCY RESPONSE of FIR AG PLOTTING vs. Frqucy PASE AGNITUDE vs. Frq PASE vs. Frq DOAINS: Tim & Frqucy Tim-Domai: tim discrt-tim sigal x(t cotiuous-tim sigal Frqucy Domai (sum of siusoids Spctrum vs. f (z ANALOG vs. DIGITAL Spctrum vs. omga-hat ov ac ad forth QUICKLY ECE- Sigal Procssig First 3 ECE- Sigal Procssig First 4
DIGITAL FILTERING x(t A-to-D FILTER D-to-A CONCENTRATE o th SPECTRU SINUSOIDAL INPUT INPUT SU of SINUSOIDS Th, OUTPUT SU of SINUSOIDS y(t FILTERING EXAPLE 6 7-poit AVERAGER y7 ( x 7 Rmovs cosi By maig its amplitud (A smallr 3-poit AVERAGER Chags A slightly y 3 ( x 3 ECE- Sigal Procssig First 7 ECE- Sigal Procssig First 8 3-pt AVG EXAPLE Iput : x (. + cos(π /8 + π / 4 for 4 7-pt FIR EXAPLE (AVG Iput : x (. + cos(π /8 + π / 4 for 4 USE PAST VALUES CAUSAL: Us Prvious ECE- Sigal Procssig First 9 ECE- Sigal Procssig First LONGER OUTPUT
ECE- Sigal Procssig First SINUSOIDAL RESPONSE INPUT: SINUSOID OUTPUT: will also a SINUSOID Diffrt Amplitud ad Phas SAE Frqucy APLITUDE & PASE CANGE Calld th FREQUENCY RESPONSE FREQUENCY RESPONSE ECE- Sigal Procssig First DCONVDEO: ATLAB GUI ECE- Sigal Procssig First 3 COPLEX EXPONENTIAL x h x y FIR DIFFERENCE EQUATION < < A x ϕ ˆ is th iput sigal a complx xpotial ECE- Sigal Procssig First 4 COPLEX EXP OUTPUT Us th FIR Diffrc Equatio A ϕ ˆ ˆ ( A x y ˆ ( ϕ A ϕ ˆ ˆ (
FREQUENCY REPONSE At ach frqucy, w ca DEFINE ( ˆ ˆ ˆ FREQUENCY RESPONSE Complx-valud formula as AGNITUDE vs. frqucy Ad PASE vs. frqucy Notatio: ˆ i plac of ( ˆ ECE- Sigal Procssig First 5 EXAPLE 6. { } {,, } + + ˆ + + ( + cos ˆ Sic ( + cos ˆ agitud is EXPLOIT SYETRY ECE- Sigal Procssig First 6 ( + cos ˆ ad Phas is ˆ PLOT of FREQ RESPONSE } { {,,} EXAPLE 6. ( + cos ˆ RESPONSE at π/3 Fid y wh ad x π / 4 ˆ ( π /3 is ow π ˆ (radias ECE- Sigal Procssig First 7 π ( + cos ˆ ECE- Sigal Procssig First 8
EXAPLE 6. (aswr Fid y wh O Stp - valuat y x ( + cos ˆ 3 π /3 π / 4 ( π /3 ECE- Sigal Procssig First 9 at ˆ π / 3 @ ˆ π / 3 π /3 π / 4 ( π /3 ( 3 6 π / ( π /3 ATLAB: FREQUENCY RESPONSE frqz(,,ww VECTOR cotais Filtr Cofficits dots IIR cofficits (usd latr ad ww is a vctor of frqucis FILTER COEFFICIENTS { } ECE- Sigal Procssig First LTI SYSTES LTI: Liar & Tim-Ivariat COPLETELY CARACTERIZED y: FREQUENCY RESPONSE, or IPULSE RESPONSE h Siusoid IN -----> Siusoid OUT At th SAE Frqucy Tim & Frqucy Rlatio Gt Frqucy Rspos from h r is th FIR cas: h IPULSE RESPONSE ECE- Sigal Procssig First ECE- Sigal Procssig First
BLOCK DIAGRAS UNIT-DELAY SYSTE Equivalt Rprstatios Fid h ad for y x h ˆ ˆ ˆ δ ˆ { } ˆ {, } ECE- Sigal Procssig First 3 ECE- Sigal Procssig First 4 FIRST DIFFERENCE SYSTE DLTI Dmo with Siusoids Fid h ad for th Diffrc Equatio : y x x FILTER δ δ ˆ ECE- Sigal Procssig First 5 ECE- Sigal Procssig First 6
CASCADE SYSTES Dos th ordr of S & S mattr? NO, LTI SYSTES ca rarragd!!! WAT ARE TE FILTER COEFFS? { } WAT is th ovrall FREQUENCY RESPONSE? δ h S h h S h h ECE- Sigal Procssig First 7 CASCADE EQUIVALENT ULTIPLY th Frqucy Rsposs EQUIVALENT SYSTE ˆ ECE- Sigal Procssig First 8 CASCADE EXAPLE FILTER SPECIFICATIONS Imag xampl igh-pass Low-pass Low-pass igh-pass ECE- Sigal Procssig First 9 ECE- Sigal Procssig First 3
CASCADE EXAPLE CASCADE EXAPLE igh-pass Low-pass Low-pass igh-pass ECE- Sigal Procssig First 3 ECE- Sigal Procssig First 3