Uniform Noise Sequences for Nonlinear System Identification

Francois Germain; Jonathan Abel; Philippe Depalle; Marcelo Wanderley
DAFx-2012 - York
Noise-based nonlinear system identification techniques using Hammerstein and Wiener forms have found wide application in biological system modeling, and been applied to modeling nonlinear audio processors such as the ring modulator. These methods apply noise to the system, and project the system output onto a set of orthogonal polynomials to reveal parameters of the model. Though Gaussian sequences are invariably used to drive the unknown system, it seems clear that the statistics of the input will affect the model estimate. Motivated by the limited input and output ranges supported by analog systems, in this work, the use of an input noise sequence having a uniform distribution is explored. In addition, an error measure indicating harmonic distortion modeling accuracy is introduced. Simulation results identifying Hammerstein and Wiener systems show that the uniform and Gaussian distributions perform differently, with the uniform distribution generally producing more accurate harmonic responses. Finally, uniform noise and Gaussian noise are used to model a saturating low-pass circuit similar to that of the Tube Screamer, with the uniform distribution providing a modest improvement in noise response error.