Separation of Nonlinear Ultrasound Signals Based on Second-Order Volterra System Identification

Abstract

This paper introduces a system identification based on second Volterra filter (SVF) as a mathematical model to separate harmonic components of a radio frequency (RF) line from a simulated nonlinear pulse–echo system (NPS). Filter coefficients of both the linear (the first-order Volterra) and quadratic (the second-order Volterra) kernels of the SVF can be determined by processing the input and output data in the frequency domain and solving a system of linear equations. Results from the validation of the approach show that while the linear kernel correctly predicts the linear output in the fundamental energy band, the quadratic kernel appropriately captures energy primarily from the second harmonic and low frequency bands. In addition, it is shown that the system identification based on the SVF is capable of separating the second order nonlinearity embedded under the level of noise signal. This is the significant advantage of the SVF approach over other static models such as linear bandpass filters. In addition, the feasibility of regularization in decreasing the number of input–output sequences used in system identification is presented.