A polynomial multiple variance method for impulse response measurement

doi:10.1016/j.sigpro.2023.108960

2023-06-01

Alberto Carini *

Riccardo Forti

Simone Orcioni

DOI：10.1016/j.sigpro.2023.108960

原文链接

查看原文

摘要

En 中文

This manuscript describes a methodology for measuring the first-order Volterra kernel of a discrete-time nonlinear system, that is, the impulse response for small signal amplitudes of the nonlinear system. In the proposed approach, multiple linear identifications are performed using the same excitation signal multiplied by different gains, and the first-order Volterra kernel is obtained from a polynomial interpo-lation of the measured values. Any linear identification method proposed in the literature can be used with this approach. The proposed approach is a multiple variance (MV) method that, in contrast to all other MV methods, aims to estimate one of the kernels of the Volterra model, the first-order kernel, with high precision. The manuscript discusses the proposed methodology, determines the mean square devia-tion (MSD) due to noise of the measured coefficients, and the value of the optimal gains that minimize the MSD. Remarkably, it is shown in the manuscript that the optimal gains assume only a reduced set of values that depends on the order of nonlinearity. The optimal number of measurements is also de-termined. The conditions under which the proposed methodology is more convenient than the classical linear methods are discussed. The experimental results demonstrate the proposed methodology and its strengths. (c) 2023 Elsevier B.V. All rights reserved.

Keyword:

Multiple variance method

Volterra filter

Impulse response measurement