Modeling High-Frequency Loudspeaker Roll-Off

Above the break frequency for the dc blockers, the response remains more or less flat until a steep roll-off begins at around 4 kHz. We will model this roll-off using a Butterworth lowpass filter with cutoff frequency at 4 kHz or less. (The main effect of listening off-axis is to reduce this cut-off frequency. For example, at 30 degrees, the roll-off begins near 1100 Hz [569].) The roll-off rate given by a Butterworth lowpass filter is dB/octave times the filter order. From looking at a number of Bode plots similar to Fig.D.15, it was judged that dB/octave is a useful compromise roll-off rate. We see a much steeper roll-off ( dB/octave) between 5 kHz and 8 kHz in Fig.D.15, and for that we can add an additional Butterworth lowpass of order 4 or 5 cutting off at 5 kHz. The broad resonance in the 2-4 kHz range can be provided using some corner resonance in this lowpass, in which case a Moog VCF (which is 4th order) is a good choice since it has separate controls for cutoff frequency and resonance .

Butterworth lowpass filters are easily designed in the plane [460].^D.14

HERE

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.