Nonlinear ultrasound system modeling based on the Volterra filter

We introduce a second Volterra filter (SVF) as a mathematical model to separate harmonic components of a radiofrequency (RF) line from a simulated nonlinear pulse-echo system (NPS). Filter coefficients of both the linear impulse response and the quadratic kernel 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 impulse response correctly predicts the linear output in the fundamental energy band, the quadratic kernel appropriately captures energy primarily from the 2^nd 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.