Frequency domain response under arbitrary excitation for fading memory nonlinear systems

For dynamic systems, the steady-state system response to periodic excitation is well understood for both linear and certain nonlinear system classes. When the excitation is not periodic, however, the measured response will contain both transient and steady-state contributions. For linear systems, these transient contributions have been thoroughly explored, while no equivalent analysis exists for the nonlinear case. In this paper, we derive an expression in the frequency domain for the system response of all discrete time-invariant nonlinear systems which have fading memory, using the Volterra series representation. The expression contains both steady-state and transient contributions at each nonlinear order, revealing a highly structured view of nonlinear system response. For the nonlinear case, the transient expressions at higher nonlinear orders have a more complex structure than those generated by linear systems, which provides valuable insight for systems theory and identification purposes. (C) 2019 Elsevier Ltd. All rights reserved.