UNIT 6 Structures of IIR Filters Topics to

UNIT – 6 Structures of IIR Filters

Topics to be covered • Direct form 1 & 2 realizations • Cascade realizations • Parallel realizations 3/2/2021

Implementation of DT Systems Types of Modeling methods: Ø Block Diagram Ø Signal Flow Graph Need of Different Structures Ø Finite-precision number representation of a digital computer. Ø Truncation or rounding error.

Basic Operations Adder x 1(n) Multiplier x(n) x 2(n) x 1(n) + x 2(n) + a ax(n) Delay element x(n) z 1 x(n 1)

Example X(n) b + y(n) z 1 + a 1 a 2 z 1

General representation of Difference equation

Implementation of FIR systems Basic Structure for FIR Systems For causal FIR systems, the system function has only zeros. Structures for Linear Phase system A generalized linear phase system satisfies: h(M n) = h(n) for n = 0, 1, …, M or h(M n) = h(n) for n = 0, 1, …, M

Direct Form x(n) z 1 h(0) z 1 h(1) z 1 h(2) h(M 1) h(M) y(n) z 1 h(0) z 1 h(1) z 1 h(2) h(M 1) h(M) x(n)

Cascade Form x(n) b 01 z 1 b 11 b 21 b 0 Ms b 02 z 1 b 12 b 22 z 1 b 1 Ms b 2 Ms y(n)

Lattice Structures Consider x(n)= (n), one will see

Example for Lattice Structure m=0 1 m=1 1 0. 6728 0. 7952 0. 9 m=2 0. 1820 0. 64 m=3 0. 576

Lattice Structure 0. 6728 0. 1820 0. 576

Implementation of IIR System Direct Form – I b 0 x(n) x(n 1) x(n 2) z 1 + y(n) + + a 1 z 1 z 1 b. M 1 z 1 x(n M) b 1 + b. M + + a. N 1 a. N y(n 1) y(n 2) z 1 y(n M)

Direct Form - II x(n) + + a 1 z 1 b 0 + b 1 + y(n) z 1 + a. N 1 a. N b. N 1 z 1 b. N + Assume M=N

Cascade Form

Cascade Form b 01 b 03 a 11 z 1 b 11 a 12 z 1 b 12 a 13 z 1 b 13 a 21 z 1 b 21 a 22 z 1 b 22 a 23 z 1 b 23 X(n) y(n)

Parallel Form

Parallel Form X(n) y(n)