Introduction
Chamberlin filter topology is frequently used in music
applications where very narrow-band, low-pass filters are
necessary. Chamberlin implementations do not suffer from some
stability problems that arise in direct-form implementations
of very narrow-band responses. For more information about
IIR/FIR filter design for DSPs, refer to the
Motorola Application Note.
Filter Topology
A Chamberlin filter is a simple two-pole IIR filter with the
transfer function given in
Equation 1:
Hz=
F
z
2z-11-2-
F
c
Q
c
-
F
c
2z-1+1-
F
c
Q
c
z-2
H
z
F
z
2
z
-1
1
2
F
c
Q
c
F
c
2
z
-1
1
F
c
Q
c
z
-2
(1)
where
Fc
F
c
determines the frequency where the filter peaks, and
Q
c
1Q
Q
c
1
Q
determines the rolloff.
Q is
defined as the positive ratio of the center frequency to the
bandwidth. A derivation and more detailed explanation is
given in
Dattorro. The
topology of the filter is shown in
Figure 1.
Note that the final feedback stage puts a pole just inside the
unit circle on the real axis. For a response with smaller
bandwidth, move the pole closer to the unit circle, but do not
move it so far that the filter becomes unstable. Multiple
second-order sections can be cascaded to yield a sharper
rolloff.
Figure 2 and
Figure 3 show how
the response of the filter varies with
Q
c
Q
c
and
F
c
F
c
.
Exercise
First, create a MATLAB script that takes two parameters,
Q
c
Q
c
and
F
c
F
c
, and plots the frequency response of a filter with a
transfer function given in
Equation 1. Then
implement a Chamberlin filter on the DSP and compare its
performance with that of your MATLAB simulation for the same
values of
Q
c
Q
c
and
F
c
F
c
. What do you observe?
References-
J. Dattorro. (1996, September). Effect Design Part 1: Reverberator and Other Filters. Journal Audio Engineering Society, vol. 45, 660-684.
-
Implementing IIR/FIR Filters with Motorola's DSP56000/SPS/DSP56001, Digital Signal Processors. [http://merchant.hibbertco.com/mtrlext/fs22/pdf-docs/motorola/apr7.rev2.pdf]. Motorola.
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