In this paper, a first-order complex bandpass filter (CBF) derived in the discrete frequency domain is proposed as a building block for the complex signal processing unit in three-phase converter systems. The first-order discrete CBF can be directly implemented in a digital system, is stable at all center frequencies, and has a low computational burden. The first-order CBF is extended to a $p$th-order discrete CBF. A normalized frequency-locked loop (FLL) is then developed that allows the frequency adaption to satisfy a desired settling time regardless of the input signal magnitude or discrete CBF form. The $p$th-order discrete CBF-FLL was tested on an FPGA in the form of two industrial applications: voltage synchronization under grid fault and extraction of an unknown frequency component. The second-order discrete CBF-FLL offered significantly improved stopband attenuation and frequency estimation relative to the first-order discrete CBF-FLL, for a small increase in computational burden.

中文翻译：

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用于三相转换器系统的离散时间复数带通滤波器

在本文中，提出了在离散频域中导出的一阶复数带通滤波器 (CBF) 作为三相转换器系统中复数信号处理单元的构建块。一阶离散CBF可以直接在数字系统中实现，在所有中心频率下都稳定，计算负担低。一阶 CBF 扩展为$p$三阶离散CBF。然后开发归一化锁频环 (FLL)，无论输入信号幅度或离散 CBF 形式如何，它都允许频率自适应满足所需的稳定时间。这$p$三阶离散 CBF-FLL 在 FPGA 上以两种工业应用的形式进行了测试：电网故障下的电压同步和未知频率分量的提取。相对于一阶离散 CBF-FLL，二阶离散 CBF-FLL 提供了显着改进的阻带衰减和频率估计，但计算负担略有增加。