DSP First, 2/e. y[n] a 1. y[n 1] a 2. y[n 2] b k. x[n k] This Lecture: Lecture 25 Second-Order IIR Filters: 3-Domains.
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1 DSP First, / Lctur 5 Scod-Ordr IIR Filtrs: 3-Domais READING ASSIGNMENTS Tis Lctur: Captr, Scts. - ad - Otr Radig: Exampl of IIR LPF i Sct. -3 POLES & ZEROS Frquc Rspos Impuls Rspos Aug 6 3-6, J McCllla & RW Scafr Aug 6 3-6, J McCllla & RW Scafr 3 LECTURE OBJECTIVES SECOND-ORDERORDER IIR FILTERS TWO FEEDBACK TERMS a a b x ( ca av COMPLEX POLES & ZEROS TREE-DOMAIN APPROAC BPFs av POLES NEAR TE UNIT CIRCLE Aug 6 3-6, J McCllla & RW Scafr 4 TREE DOMAINS for IIR b a Z-TRANSFORM-DOMAIN: pols & ros TIME-DOMAIN DIFFERENCE EQN N a,bb a b x M POLYNOMIALS: ( ( jˆ ˆ Us ( to gt Frq. Rspos FREQ-DOMAIN j ˆ M b N a j ˆ Aug 6 3-6, J McCllla & RW Scafr 5 jˆ
2 SECOND-ORDER ORDER FILTERS MORE POLES Two FEEDBACK TERMS a a b x b x b b a a b b x Domiator is QUADRATIC Pols: REAL or COMPLEX CONJUGATES b b a b a b b b a a Aug 6 3-6, J McCllla & RW Scafr 6 Aug 6 3-6, J McCllla & RW Scafr 7 TWO COMPLEX POLES Fid Impuls Rspos? Ca OSCILLATE vs. RESONANCE ( p ( r Fid FREQUENCY RESPONSE Dpds o Pol Locatio Clos to t Uit Circl? r j j pol r Ma BANDPASS FILTER? r j Ivrs -Trasform? SECOND-ORDERORDER IIR FILTERS ( ca av COMPLEX POLES & ZEROS ( j / 3 j / 3 Pols :.9 j / 3 Aug 6 3-6, J McCllla & RW Scafr 8 Aug 6 3-6, J McCllla & RW Scafr 9
3 d ORDER EXAMPLE j / 3 j / 3 (.9 cos( u (.9 ( u j / 3 j.9.9 ( / 3.9 cos( / 3 j / 3 j / 3 (.9 ( Aug 6 3-6, J McCllla & RW Scafr d ORDER EX: -Domai x.45x aa =, -.9,.8 ; bb =, -.45 ; = -:9; = filtr( bb, aa, (== ; = frq( bb, aa, -pi,pi/:pi pi/:pi ; Aug 6 3-6, J McCllla & RW Scafr : Dcas & Oscillats PERIOD =6 u (.9 cos Aug 6 3-6, J McCllla & RW Scafr d ORDER Z-trasform PAIRS r cos( ( u Ar cos( u GENERAL ENTRY for -Trasform TABLE r cos( r cos( r cos( r cos( r cos( r Aug 6 3-6, J McCllla & RW Scafr 3
4 Complx POLE-ZERO PLOT.75 UNIT CIRCLE MAPPING BETWEEN ad ˆ jˆ j ˆ j ˆ ˆ Aug 6 3-6, J McCllla & RW Scafr 4 FREQUENCY RESPONSE from POLE-ZERO PLOT.75 j ˆ j ˆ ( j ˆ Aug 6 3-6, J McCllla & RW Scafr 5 : Dcas & Oscillats PERIOD =6 Aug 6 3-6, J McCllla & RW Scafr 6 u (.9 cos Aug 6 3-6, J McCllla & RW Scafr 7
5 Complx POLE-ZERO PLOT Wr is t pa? : Dcas & Oscillats PERIOD = Aug 6 3-6, J McCllla & RW Scafr 8 Complx POLE-ZERO PLOT u (.95 cos Aug 6 3-6, J McCllla & RW Scafr 9 3 DOMAINS MOVIE: IIR Wr is t pa? POLE MOVES ( ( Aug 6 3-6, J McCllla & RW Scafr Aug 6 3-6, J McCllla & RW Scafr
6 CASCADE: Pol-Zro o Cacllatio at YouTub Lis: (t Multipl t -trasforms x v v ( ( x.5x x u (.5 u.5x? Follow som lis, ad s (t i actio Maf Lwis films - Voic Bras Glass w/ Tara Busc ttp:// Sow t vido abov first, t t lab masurmts blow ow to bra a wi glass wit soud Lab Masurmts ttp:// com/watc?v=jim6atnlxx4&fatur=rlatd rlatd Idia Tmpl (Dmo of cagig frquc cott i a imag: ttp:// Aug 6 3-6, J McCllla & RW Scafr Pig, Rig & Sig Aug 6 3-6, J McCllla & RW Scafr 3 Tim Domai (t FFT Braig a Wi Glass b Sigigi Pig Rig Wat is t iput? Wat ar ou masurig? Tiig (Procssig Sig Wat is t iput? Aug 6 3-6, J McCllla & RW Scafr 4 Aug 6 3-6, J McCllla & RW Scafr 5
7 Fourir Domai (FFT Rcall Frquc Rspos Siusoid-i givs siusoid-outout Tru for LTI sstms Sms to rquir a ifiit-lgt siusoid x cos( ˆ Output is ( for cos( ˆ j ˆ for Similar for ral-world siusoids startig at = cos( ˆ x cos( ˆ u Aug 6 3-6, J McCllla & RW Scafr 6 Aug 6 3-6, J McCllla & RW Scafr 7
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