Analytical Reconstruction of the Nonlinear Transfer Function for a Wiener–Hammerstein Model

In the present contribution, we proposed a novel approach for digital amplifier simulation and signal modulation in audio engineering applications. To this end, input and output signals are superimposed to produce a Lissajous curve, which contains nonlinear effects from amplification and further phase shifts from linear equalization filters. Here, the challenge is to identify the nonlinearity. From experimental data, a time sequence was used for the analysis that formed a closed Lissajous figure, which provided the spectrum together with the phase shifts of the output signal by fitting the data. A representation for the nonlinear transfer function was obtained upon setting the phase shifts to zero in the reconstructed output signal upon using the developed analytical expressions for the amplitude and phase shifts. For three considered nonlinear transfer functions, the method showed a fairly good similarity in comparison to the original output signals. The developments were further applied to a set of different input frequencies in order to analyze this influence on the quality of profiling the nonlinearity. Input frequencies in the range where the linear filters had only small effects provided acceptable results for the nonlinear transfer function. Finally, possible future developments and improvements of the proposed approach are presented.