Discretization of the ’59 Fender Bassman Tone Stack

The market for digital modeling guitar amplifiers requires that the digital models behave like the physical prototypes. A component of the iconic Fender Bassman guitar amplifier, the tone stack circuit, filters the sound of the electric guitar in a unique and complex way. The controls are not orthogonal, resulting in complicated filter coefficient trajectories as the controls are varied. Because of its electrical simplicity, the tone stack is analyzed symbolically in this work, and digital filter coefficients are derived in closed form. Adhering to the technique of virtual analog, this procedure results in a filter that responds to user controls in exactly the same way as the analog prototype. The general expressions for the continuous-time and discrete-time filter coefficients are given, and the frequency responses are compared for the component values of the Fender ’59 Bassman. These expressions are useful implementation and verification of implementations such as the wave digital filter.