We derive the entropy rate formula for a complex Gaussian random process by using a widely linear model. The resulting expression is general and applicable to both circular and noncircular Gaussian processes, since any second-order stationary process can be modeled as the output of a widely linear system driven by a circular white noise. Furthermore, we demonstrate application of the derived formula to an order selection problem. We extend a scheme for independent and identically distributed (i.i.d.) sampling to the complex domain to improve the estimation performance of information-theoretic criteria when samples are correlated. We show the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging (fMRI) data that are inherently complex valued.

中文翻译：

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复域熵率及其在iid采样中的应用

我们通过使用广泛的线性模型推导出复杂高斯随机过程的熵率公式。结果表达式是通用的，适用于圆形和非圆形高斯过程，因为任何二阶平稳过程都可以建模为由圆形白噪声驱动的宽线性系统的输出。此外，我们展示了导出公式在订单选择问题中的应用。我们将独立同分布 (iid) 采样的方案扩展到复杂域，以提高样本相关时信息论标准的估计性能。我们展示了对固有复值的模拟和实际功能磁共振成像 (fMRI) 数据进行顺序选择的方法的有效性。