Computationally efficient nonlinear Chebyshev models using common-pole parallel filters with the application to loudspeaker modeling

摘要

Many audio systems show some form of nonlinear behavior that has to be taken into account in modeling. For this, often a black-box model is identified, coming from the generality and simplicity of the approach. One such model is the polynomial Hammerstein model, which uses parallel branches that have a polynomial-type nonlinearity and a linear filter in series. For example, Chebyshev models use Chebyshev polynomials as nonlinear functions, making model identification a very straightforward procedure by logarithmic swept-sine measurements. This paper proposes a highly efficient implementation of Chebyshev models by using fixed-pole parallel filters for the linear filtering part. The efficiency comes both from using common-pole modeling and from applying a warped filter design that takes into account the frequency resolution of hearing. Due to its efficiency, the proposed model is particularly well suited for the real-time digital simulation of weakly nonlinear devices, such as amplifiers, nonlinear effects, or tube guitar amplifiers.