Non-linear output frequency response functions for multi-input non-linear Volterra systems

Abstract

Abstract:The concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the nonlinear systems that can be described by a multi-input Volterra series model. A new algorithm is also developed to determine the output frequency range of nonlinear systems from the frequency range of the inputs. These results allow the concept of NOFRFs to be applied to a wide range of engineering systems. The phenomenon of the energy transfer in a two degree of freedom nonlinear system is studied using the new concepts to demonstrate the significance of the new results.

On the distribution of nonlinear effects in locally nonlinear one-dimensional chain type structures

“…Great efforts have been made to develop various sophisticated theories and approaches to tackle the nonlinear problems, such as the time domain methods including the perturbation method [47,48], multiple scale method [49], KBM method [50], etc. and the frequency domain methods including the Generalized Frequency Response Function (GFRF) [41,45,51,52], the Nonlinear Output Frequency Response Function (NOFRF) [33,34,[53][54][55], the Describing Function Method [56] and the harmonic balance method [36,57], etc. There are a great number of literatures available about the nonlinear system analysis using above methods, and most of them are focused on investigating how the nonlinear characteristic parameters k n k L-1 k 1…”

Low complexity predistortion and equalization in nonlinear multicarrier satellite communications

“…This theory has been extended to multiple input multiple output systems (MIMO) in [31][32][33]. However, it is convenient to describe the Volterra series in discrete complex baseband representation as in [6,34] since communication signals are denoted and manipulated in this domain.…”

“…However, it is convenient to describe the Volterra series in discrete complex baseband representation as in [6,34] since communication signals are denoted and manipulated in this domain. The continuous time MIMO Volterra [31][32][33] and the complex base-band formalism [34] were combined in [23], in which a complex 2 × 2 Volterra system was formulated. Extending that results to an arbitrary number of carriers, we get:…”

Combating the dimensionality of nonlinear MIMO amplifier predistortion by basis pursuit

“…A K × K nonlinear dynamic MIMO system can be described as K MISO (multiple input single ouput) systems [11]. The Volterra series for a MIMO system with complex baseband signals is described as [4]:…”