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Published byDarrell Lesley Hunt Modified over 9 years ago
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Analysis and Implementation of the Guitar Amplifier Tone Stack
David Yeh, Julius Smith CCRMA Stanford University Stanford, CA
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Digital audio effects that emulate analog equipment are popular
“Modeling” amplifiers Products by Line 6, Yamaha, Roland, Korg, Universal Audio, etc. CAPS open source LADSPA suite Emulate behavior of classic analog gear in software As close to real thing as possible For portability and flexibility
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Guitar amp tone stack is a unique component in the sound of an amplifier
Almost every guitar amplifier, solid state or tube, has a tone control circuit – referred to as a tone stack Passive RC filter to audio signal Located either directly after preamp stage or after stages of gain and buffer
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Prior work Modeled by Line 6 (and others)
Analyzed by Kuehnel (2005, book) Substituted in CAPS (LADSPA plugins for guitar effects) by shelving filter
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Parameter mapping from tone controls to frequency response is very complicated
Passive RC circuit Three real poles One zero at DC, one pair of zeros with anti-resonance Shelving filter is close: 3 poles, 3 zeros Frequency response depends on pole locations But no notch filtering Circuit components are not isolated Component values are comparable Bridge topology Tone controls affect location of multiple poles and zeros
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Tone Stack Transfer Function
Third order continuous time system Complex mapping from component values/parameters to coefficients
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Poles depend only on Bass and Mid controls
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Zeros depend on all parameters
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Poles sweeping Bass and Mid
Low freq Pole 1 Pole 2 Pole 3 High freq
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Zeros plots for parameter sweeps
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Digitization as third-order filter
Straightforward approach Find continuous time transfer function Discretize by bilinear transform Implement as transposed Direct Form II (DFII) Pros: Perfect mapping of tone controls to frequency response within limitations of bilinear transform Cons: Complicated formulas to compute coefficients
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Bilinear transformation of 3rd order system
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DFII block diagram Audio in Treble Compute DF coefs B[]
Component values R, C Treble Compute DF coefs B[] Transposed DFII core A[] Mid Bass Audio out
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DFII frequency response shows good match with continuous time version
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Error relative to continuous time
Worst case errors shown B=1, M=0, T=0 Discrete time reaches low pass asymptote but continuous time does not
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Reduced sampling rate Commercial effects pedals commonly run at 31 kHz
Guitar amplifier system is bandlimited by speaker response: 100–6000 Hz. For f_s = 20 kHz, error increases but only at high frequency because of asymptotic limits
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Table lookup implementation simplifies computation of coefficients
Lattice filter implementation for robustness to roundoff error in coefficients and to smoothly fade between coefficients as tone controls are varied Tabulate 25 steps of each tone control parameter Convert from z-domain transfer function to lattice coefficients by step-down algorithm Implemented DFII and lattice filter in CAPS audio suite. Both run in real time.
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White noise at different settings
Sound samples White noise at different settings Original white noise (2 sec) B=0 M=0 T=0 B=0 M=1 T=0 B=1 M=0 T=1 B=1 M=1 T=0 B=1 M=1 T=1 B=0.5 M=1 T=0.5
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Comparison of implementations
DFII Table lookup Exact parameterization of tone stack behavior “ Runs in real time More efficient computation of filter coefficients Arbitrary precision of tone settings Settings are quantized – can interpolate Easy to change circuit component values Must tabulate each circuit configuration Real time changes in tone settings not audible Robust to roundoff errors in coefficients – can fade between settings
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