Fourier expansion of hammerstein models for nonlinear acoustic system identification

We consider the task of acoustic system identification, where the input signal undergoes a memoryless nonlinear transformation before convolving with an unknown linear system. We focus on the possibility of modeling the nonlinearity with different basis functions, namely the established power series and the proposed Fourier expansion. In this work the unknown coefficients of generic basis functions are merged with the unknown linear system to obtain an equivalent multichannel structure. We use a multichannel DFT-domain algorithm for learning the underlying coefficients of both types of basis functions. We show that the Fourier modeling achieves faster convergence and better learning of the underlying nonlinearity than the polynomial basis.