TY  - GEN
U1  - Sonstiges
A1  - Franz, Matthias O.
T1  - Volterra and Wiener series
T2  - Scholarpedia
N2  - Volterra and Wiener series are two classes of polynomial representations of nonlinear systems. They are perhaps the best understood and most widely used nonlinear system representations in signal processing and system identification. A Volterra or Wiener representation can be thought of as a natural extension of the classical linear system representation. In addition to the convolution of the input signal with the system's impulse response, the system representation includes a series of nonlinear terms that contain products of increasing order of the input signal with itself. It can be shown that these polynomial extension terms allow for representing a large class of nonlinear systems which basically encompasses all systems with scalar outputs that are time-invariant and have noninfinite memory.
KW  - System identification
KW  - Kernel based learning
Y1  - 2011
UR  - http://www.scholarpedia.org/article/Volterra_and_Wiener_series
U6  - https://doi.org/doi:10.4249/scholarpedia.11307
DO  - https://doi.org/doi:10.4249/scholarpedia.11307
IS  - 6(10):11307
ER  -