文档介绍：Basic IIR Digital Filter Basic IIR Digital Filter
Structures Structures
• The causal IIR digital filters we are • An N-th order IIR digital transfer function is
concerned with in this course are characterized by 2N+1 unique coefficients,
characterized by a real rational transfer
­1 and in general, requires 2N+1 multipliers
function of z or, equivalently by a constant and 2N two-input adders for implementation
coefficient difference equation
• From the difference equation representation, • Direct form IIR filters: Filter structures in
it can be seen that the realization of the which the multiplier coefficients are
causal IIR digital filters requires some form precisely the coefficients of the transfer
of feedback function
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Direct Form IIR Digital Filter Direct Form IIR Digital Filter
Structures Structures
• Consider for simplicity a 3rd-order IIR filter W(z)
H ( z)
with a transfer function X (z) H1(z) 2 Y(z)
P(z) p + p z­1 + p z­2 + p z­3 where
H (z) = = 0 1 2 3
D(z) ­1 ­2 ­3 W(z)
1 + d1z + d2z + d3z H (z) = = P(z) = p + p z­1 + p z­2 + p z­3
1 X (z) 0 1 2 3
• We can implement H(z) as a cascade of two Y (z) 1 1
H (z) = = =
filter sections as shown on the next slide 2 ­1 ­2 ­3
W (z) D(z) 1+ d1z + d2z + d3z
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Direct Form IIR Digital Filter Direct Form IIR Digital Filter
Structures Structures
• The filter section H 1 ( z ) can be seen to be • The time-domain representation of H 2 ( z ) is
an FIR filter and can be realized as shown given by
below y[n] = w[n] ­ d1y[n ­1]­ d2 y[n ­ 2] ­ d3y[n ­3]
w[n] = p x[n] + p x[n ­ 1] + p x[n ­ 2] + p x[n ­ 3]
0 1 2 3 Realization of H2(z)
follows from the
above equation
and is shown on
the right
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1
Direct Form IIR Digital Filter Direct Form IIR Digital Filter
Structures S