The paper introduces a novel family of deterministic periodic signals, the orthogonal periodic sequences (OPSs), that allow the perfect identification on a finite period of any functional link polynomials (FLiP) filter with the cross-correlation method. The class of FLiP filters is very broad and includes many popular nonlinear filters, as the well-known Volterra and the Wiener nonlinear filters. The novel sequences share many properties of the perfect periodic sequences (PPSs). As the PPSs, they allow the perfect identification of FLiP filters with the cross-correlation method. But, while PPSs exist only for orthogonal FLiP filters, the OPSs allow also the identification of non-orthogonal FLiP filters, as the Volterra filters. In OPSs, the modeled system input can be any persistently exciting sequence and can also be a quantized sequence. Moreover, OPSs can often identify FLiP filters with a sequence period and a computational complexity much smaller that PPSs. The provided experimental results, involving the identification of real devices and of a benchmark model, highlight the potentialities of the proposed OPSs in modeling unknown nonlinear systems.

中文翻译：

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用于识别功能链路多项式滤波器的正交周期序列


本文介绍了一系列新颖的确定性周期信号，即正交周期序列 (OPS)，它允许使用互相关方法对任何函数链接多项式 (FLiP) 滤波器的有限周期进行完美识别。 FLiP 滤波器的类别非常广泛，包括许多流行的非线性滤波器，如众所周知的 Volterra 和 Wiener 非线性滤波器。这些新颖的序列具有完美周期序列（PPS）的许多特性。作为 PPS，它们允许使用互相关方法完美识别 FLiP 滤波器。但是，虽然 PPS 仅适用于正交 FLiP 滤波器，但 OPS 还允许识别非正交 FLiP 滤波器，如 Volterra 滤波器。在OPS中，建模的系统输入可以是任何持续令人兴奋的序列，也可以是量化的序列。此外，OPS 通常可以识别具有序列周期的 FLiP 滤波器，并且计算复杂度比 PPS 小得多。所提供的实验结果涉及真实设备和基准模型的识别，突出了所提出的 OPS 在建模未知非线性系统方面的潜力。