Volterra series transfer function of single-mode fibers

Traditional measurement of multimedia systems, e.g. linear impulse response and transfer function, are sufficient but not faultless. For these methods the pure linear system is considered and nonlinearities, which are usually included in real systems, are disregarded. One of the ways to describe and analyze a nonlinear system is by using Volterra Series representation. However, this representation uses an enormous number of coefficients. In this work a simplification of this method is proposed and an experiment with an audio amplifier is shown.

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A Simulation Platform for Multi-Channel Transmission Systems in Frequency Domain Using Volterra Series Transfer Function

Optical Communications and Networks ◽

10.1142/9789812776280_0099 ◽

2002 ◽

Author(s):

Ken Kai-fu Chang ◽

Le Nguyen Binh

Keyword(s):

Transfer Function ◽

Frequency Domain ◽

Volterra Series ◽

Simulation Platform ◽

Transmission Systems

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Transfer Function with Nonlinear Characteristics Definition Based on Multidimensional Laplace Transform and its Application to Forced Response Power Systems

Energies ◽

10.3390/en12214061 ◽

2019 ◽

Vol 12 (21) ◽

pp. 4061

Author(s):

Villalón ◽

Medina-Rios

Keyword(s):

Transfer Function ◽

Power Systems ◽

Power System ◽

Laplace Transform ◽

Frequency Response ◽

Transfer Functions ◽

Volterra Series ◽

Forced Response ◽

Nonlinear Characteristics ◽

Test Power

In this research, the concept of nonlinear transfer function with nonlinear characteristics is introduced through the multidimensional Laplace transform and modal series (MS) method. The method of modal series is applied to the power systems dynamics analysis in order to consider nonlinear oscillations and modal interactions, which contribute to the response of the system's dynamic following disturbances. The method of MS allows the inclusion of input excitation functions obtained as Laplace domain kernels superposed to obtain a transfer function. Applying the Volterra series expansion through kernels decomposition, a transfer function with nonlinear characteristics is obtained which incorporates some of the main modal characteristics of the nonlinear system. Following the same schematic procedure, it is possible to determine second and higher order transfer functions. Once the transfer functions both linear and with nonlinear characteristics are determined, a time domain and frequency response analyses can be performed. The methodology is exemplified by denoting the numerical and analytical properties with the application to a synchronous machine-infinite busbar test power system and to a three synchronous machines–nine buses test power system. Bode and Nyquist analysis are utilized to demonstrate the transfer functions accuracy and frequency response.

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