The Fourier series is introduced as a transfer function (TF) in the artificial neural network (ANN) for parametric modeling of microwave filters in this letter. The reported pole-residue-based TF leads to an order-changing problem of input samples from vector fitting, which is usually solved with an order-tracking technique or data classification. The proposed Fourier series-based TF does not have to carry out the time-consuming operation because the only coefficient order can be determined for all input samples in an iterative process. Compared with the pole-residue-based TF, moreover, the ANN training involves a small number of TF coefficients in the proposed method. The predicted electromagnetic (EM) response is obtained from the coefficients of the ANN output. An example of the ultrawideband (UWB) filter is employed to verify the effectiveness of the Fourier series-based TF.

中文翻译：

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具有用于滤波器建模的基于傅立叶级数的传递函数的神经网络


在这封信中，傅立叶级数被作为人工神经网络 (ANN) 中的传递函数 (TF) 引入，用于微波滤波器的参数化建模。所报道的基于极点残差的 TF 会导致矢量拟合中输入样本的顺序变化问题，该问题通常通过顺序跟踪技术或数据分类来解决。所提出的基于傅里叶级数的 TF 不必执行耗时的操作，因为可以在迭代过程中为所有输入样本确定唯一的系数阶。此外，与基于极点残差的 TF 相比，该方法中的 ANN 训练涉及少量的 TF 系数。预测的电磁 (EM) 响应是从 ANN 输出的系数获得的。采用超宽带 (UWB) 滤波器的示例来验证基于傅里叶级数的 TF 的有效性。