Musical distortion circuits, especially guitar amplifiers, have been the subject of virtual analog modeling for years. There exists two main modeling approaches: white-box modeling, where the internal properties are fully known, and gray-box modeling, where only the input and output are available. This work proposes a gray-box modeling approach for analog guitar amplifiers using iterative optimization to adjust the parameters of a block-based model. The only assumption made about the reference system is its basic structure. The digital model is an extended Wiener–Hammerstein model consisting of a linear time-invariant (LTI) block, a nonlinear block with a nonlinear mapping function, and another LTI block connected in series. The model is adapted in two steps: first the filters are measured, and then the parameters for the nonlinear part of the digital model are optimized with the Levenberg–Marquardt method to minimize a cost-function describing the error between the digital model and the analog reference system. A small number of guitar amplifiers were modeled, the adapted model was evaluated with objective scores, and a listening test was performed to rate its quality.
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