Ch6(3) Tunable IIR Digital Filters.pdf

Tunable Lowpass and
Tunable IIR Digital Filters Highpass Digital Filters
• We have shown earlier that the 1st-order
• We have described earlier two 1st-order and lowpass transfer function
two 2nd-order IIR digital transfer functions
1­ aæ 1 + z­1 ö
with tunable frequency response H (z) = ç ÷
LP ç ­1 ÷
characteristics 2 è1­ a z ø
• We shall show now that these transfer and the 1st-order highpass transfer function
functions can be realized easily using 1+ a æ 1­ z­1 ö
ç ÷
HHP (z) = ç ­1 ÷
allpass structures providing independent 2 è1 ­ a z ø
tuning of the filter parameters are plementary pair
1 Copyright © 2001, S. K. Mitra 2 Copyright © 2001, S. K. Mitra
Tunable Lowpass and
Tunable Lowpass and
Highpass Digital Filters
Highpass Digital Filters
• A realization of H LP ( z ) and H HP ( z ) based
• Moreover, they can be expressed as on the allpass-based position is
H (z) = 1[1 + A ( z)] shown below
LP 2 1
HHP (z)
H (z) = 1[1­ A (z)]
HP 2 1
where
­ a + z­1 • The 1st-order allpass filter can be realized
A1(z) = using any one of the 4 single-multiplier
1­ a z­1
is a 1st-order allpass transfer function allpass structures described earlier
3 Copyright © 2001, S. K. Mitra 4 Copyright © 2001, S. K. Mitra
Tunable Lowpass and Tunable Lowpass and
Highpass Digital Filters Highpass Digital Filters
• One such realization is show