Modeling a Twelve-Inch Guitar Speaker

The measured amplitude response of a 12" ``Celestion G12'' guitar speaker is available at professional.celestion.com.^D.13Figure D.15 shows the measured amplitude response from their data sheet.

The octave-forge function invfreqz can be used conjunction with the function minphaseir included with [49] (and listed in Fig.D.23 below) to obtain a digital filter that approximates the response of a guitar speaker. This filter, whatever order is chosen, can be converted to series second-order sections by the octave-forge function tf2sos, and each section can be implemented using function TF2 defined in Faust's music.lib. While this is a very general method that can be adapted to many problems (especially when the error-versus-frequency weighting is carefully chosen), here we will do a ``direct'' design based on inspection of the response.

In classical control system design [129], a commonly used tool is the Bode plot (or Bode diagram), which is a plot of the log-magnitude frequency response versus log frequency, as in Fig.D.15. On such a plot, each transfer-function zero near the axis contributes dB/octave to the amplitude response at frequencies above the zero, and each pole contributes dB/octave. This was already applied in §D.2.5 above. We now take the same approach to obtaining a qualitative match to the 12" speaker response in Fig.D.15.

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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