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SPFirst-L18 - Signal Processing First READING ASSIGNMENTS...

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4/18/2004 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 18 3-Domains for IIR 4/18/2004 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS This Lecture: Chapter 8, all Other Reading: Recitation: Ch. 8, all POLES & ZEROS Next Lecture: Chapter 9 4/18/2004 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES SECOND-ORDER IIR FILTERS TWO FEEDBACK TERMS H(z) can have COMPLEX POLES & ZEROS THREE-DOMAIN APPROACH BPFs have POLES NEAR THE UNIT CIRCLE y [ n ] = a 1 y [ n 1] + a 2 y [ n 2] + b k x [ n k ] k = 0 2 4/18/2004 © 2003, JH McClellan & RW Schafer THREE DOMAINS a A , b k { } Z-TRANSFORM-DOMAIN: poles & zeros POLYNOMIALS: H(z) Use H(z) to get Freq. Response z = e j ˆ ω H ( z ) = b k z k 1 a A z A FREQ-DOMAIN A A A ω ω ω ˆ 1 ˆ 0 ˆ 1 ) ( j N k j M k k j e a e b e H = = = TIME-DOMAIN = = + = M k k N k n x b n y a n y 0 1 ] [ ] [ ] [ A A A
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4/18/2004 © 2003, JH McClellan & RW Schafer 6 Z-TRANSFORM TABLES 4/18/2004 © 2003, JH McClellan & RW Schafer 7 SECOND-ORDER FILTERS Two FEEDBACK TERMS y [ n ] = a 1 y [ n 1] + a 2 y [ n 2] + b 0 x [ n ] + b 1 x [ n 1] + b 2 x [ n 2] H ( z ) = b 0 + b 1 z 1 + b 2 z 2 1 a 1 z 1 a 2 z 2 4/18/2004 © 2003, JH McClellan & RW Schafer 8 MORE POLES Denominator is QUADRATIC 2 Poles: REAL or COMPLEX CONJUGATES H ( z ) = b 0 + b 1 z 1 + b 2 z 2 1 a 1 z 1 a 2 z 2 = b 0 z 2 + b 1 z + b 2 z 2 a 1 z
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