Efficient Realization for Third-Order Volterra Filter Based on Singular Value Decomposition

Nonlinear distortion in loudspeaker systems degrades sound quality and must be properly compensated for by linearization techniques. One technique to reduce nonlinear distortion is to use a Volterra Filter, which approximates the nonlinearity of the target loudspeaker using the Volterra series expansion. In general, the Volterra Filter is computationally very expensive, and the amount of computation needs to be reduced for real-time processing. In this paper, we propose an efficient implementation of the third-order Volterra filter based on singular value decomposition. The proposed method determines the necessary coefficients based on the symmetry of the third-order Volterra filter and applies singular value decomposition to them. In the filter structure consisting of singular values and their corresponding singular vector, the computational complexity of the third-order Volterra filter can be reduced by eliminating the part of the filter with small singular values. By focusing on the magnitude of the singular values, the proposed method can improve the computational efficiency of the third-order Volterra filter without decreasing its approximation accuracy. Simulation results show that the proposed method can improve the computational efficiency by 60% while maintaining the nonlinear distortion compensation performance of the micro-speaker for smartphones by about 8 dB.