Iir Filter

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Submitted By alay1174
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IIR Filter structures
ELG6163 Miodrag Bolic

1

Copyright © 2005, S. K. Mitra

Objective
• Stuctures
– Direct form – Transposed direct form – Lattice-ladder form – Parallel realization – Cascade realization – Bi-quad coupled realization – State space realization


2

Implementation
Copyright © 2005, S. K. Mitra

Basic IIR Digital Filter Structures
• The causal IIR digital filters we are concerned with in this course are characterized by a real rational transfer function of z −1 or, equivalently by a constant coefficient difference equation • From the difference equation representation, it can be seen that the realization of the causal IIR digital filters requires some form of feedback
3
Copyright © 2005, S. K. Mitra

Basic IIR Digital Filter Structures
• An N-th order IIR digital transfer function is characterized by 2N+1 unique coefficients, and in general, requires 2N+1 multipliers and 2N two-input adders for implementation • Direct form IIR filters: Filter structures in which the multiplier coefficients are precisely the coefficients of the transfer function
4
Copyright © 2005, S. K. Mitra

Direct Form IIR Digital Filter Structures
• Consider for simplicity a 3rd-order IIR filter with a transfer function
−1 −2 −3

P( z ) p0 + p1z + p2 z + p3 z = H ( z) = D( z ) 1 + d1z −1 + d 2 z − 2 + d3 z −3

• We can implement H(z) as a cascade of two filter sections as shown on the next slide
5
Copyright © 2005, S. K. Mitra

Direct Form IIR Digital Filter Structures
X (z )

H1 (z )

W (z )

H 2 (z )

Y (z )

where
W ( z) −1 −2 −3 H1( z ) = = P( z ) = p0 + p1z + p2 z + p3 z X ( z) Y ( z) 1 1 H 2 ( z) = = = W ( z ) D( z ) 1 + d1z −1 + d 2 z − 2 + d3 z −3
6
Copyright © 2005, S. K. Mitra

Direct Form IIR Digital Filter Structures
• The filter section H1(z ) can be seen to be an FIR filter and can be realized as shown…...

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