m10479 Surround Sound: Chamberlin Filters 2.15 2002/02/01 2009/06/03 15:35:36.173 GMT-5 Douglas L. Jones Douglas L. Jones dl-jones@uiuc.edu Swaroop Appadwedula Swaroop Appadwedula appadwed@uiuc.edu Matthew J. Berry Matthew Berry mjberry@uiuc.edu Mark A. Haun Mark Haun markhaun@uiuc.edu Jake Janevitz Jake Janovetz jake@janovetz.com Michael L. Kramer Michael Kramer kramer@ifp.uiuc.edu Dima Moussa Dima Moussa dmoussa@uiuc.edu Daniel Grobe Sachs Daniel Sachs sachs@uiuc.edu Brian Wade Brian Wade bwade@uiuc.edu Douglas L. Jones Douglas L. Jones dl-jones@uiuc.edu Swaroop Appadwedula Swaroop Appadwedula appadwed@uiuc.edu Matthew J. Berry Matthew Berry mjberry@uiuc.edu Mark A. Haun Mark Haun markhaun@uiuc.edu Daniel Grobe Sachs Daniel Sachs sachs@uiuc.edu Mike Russell Mike Russell merussel@uiuc.edu Mark D. Butala Mark Butala butala@uiuc.edu Robert L. Morrison Robert Morrison rlmorris@uiuc.edu Douglas L. Jones Douglas L. Jones dl-jones@uiuc.edu Swaroop Appadwedula Swaroop Appadwedula appadwed@uiuc.edu Matthew J. Berry Matthew Berry mjberry@uiuc.edu Mark A. Haun Mark Haun markhaun@uiuc.edu Jake Janevitz Jake Janovetz jake@janovetz.com Michael L. Kramer Michael Kramer kramer@ifp.uiuc.edu Dima Moussa Dima Moussa dmoussa@uiuc.edu Daniel Grobe Sachs Daniel Sachs sachs@uiuc.edu Brian Wade Brian Wade bwade@uiuc.edu Chamberlin DSP filter IIR low-pass music narrow-band Science and Technology The Chamberlin filter topology can implement very narrow-band, low-pass filters. This module provides the Chamberlin filter transfer function, an illustration of the topology, and sample frequency responses for different choices of design parameters. en

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.

A Chamberlin filter is a simple two-pole IIR filter with the transfer function given in : 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 where F c determines the frequency where the filter peaks, and 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 . 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.

Chamberlin Filter Topology

and show how the response of the filter varies with Q c and F c .

Chamberlin filter responses for various Q c ( F c .3 )

Chamberlin filter responses for various F c ( Q c .8333 )

First, create a MATLAB script that takes two parameters, Q c and F c , and plots the frequency response of a filter with a transfer function given in . 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 and F c . What do you observe?

J. Dattorro Effect Design Part 1: Reverberator and Other Filters Journal Audio Engineering Society 1996 vol. 45 660-684 September Implementing IIR/FIR Filters with Motorola's DSP56000/SPS/DSP56001, Digital Signal Processors Motorola http://merchant.hibbertco.com/mtrlext/fs22/pdf-docs/motorola/apr7.rev2.pdf