RealSimPLE Project Home Page at CCRMA

Making Virtual Electric Guitars and Associated Effects Using Faust

Distortion and Amplifier Feedback

Distortion and Amplifier Feedback

Faust Implementation

RealSimPLE Project Home Page at CCRMA

Making Virtual Electric Guitars and Associated Effects Using Faust

Distortion and Amplifier Feedback

Distortion and Amplifier Feedback

Faust Implementation

Cubic Nonlinear Distortion

To minimize aliasing, it is helpful to use nonlinearities that are approximated by polynomials of low order. An often-used cubic nonlinearity is given by [17]

$$f(x) = \left\{\begin{array}{ll} -\frac{2}{3}, & x\leq -1 \\ [5pt] x-\frac{x^3}{3}, & -1 < x < 1 \\ [5pt] \frac{2}{3}, & x\geq 1. \\ \end{array} \right. \protect$$ (6)

and diagrammed in Fig.11.¹³ An input gain may be used to set the desired degree of distortion. Analysis of spectral characteristics and associated aliasing due to nonlinearities appears in [14]. As discussed there, a non-saturating cubic nonlinearity does not alias at all when the input signal is oversampled by 2 or more and the nonlinearity is followed by a half-band lowpass filter, which eliminates aliasing since it is confined to the upper half-spectrum between $\pi/2$ and $\pi$ rad/sample. High quality commercial guitar distortion simulators are said to use oversampling factors of 4 to 8.

Figure 11: Soft-clipper defined by Eq.$\,$(6).

The cubic nonlinearity, being an odd function, produces only odd harmonics. To break the odd symmetry and bring in some even harmonics, a simple input offset can be used [10]. It was found empirically that a dc blocker [12] was needed to keep the signal properly centered in the output dynamic range. Since amplifier loudspeakers have a $+12$ dB/octave low-frequency response, at least two dc blockers are appropriate anyway.

While the cubic nonlinearity is the odd nonlinearity with the least aliasing (thereby minimizing oversampling and guard-filter requirements), it is sometimes criticized as overly weak as a nonlinearity, unless driven into the hard-clipping range where it is no longer bandlimited to three times the input signal bandwidth.