陷波频率精确可调的FIR稀疏多频陷波器设计算法研究

陷波器在通信技术、生物工程、雷达声纳、测量仪器等领域的应用非常广泛，它可以有效滤除特定的极窄频段的频率成分干扰，而对该频段之外的信号高效传输。本项目将研究陷波频率精确可调的稀疏FIR多频陷波器的设计算法，首次提出将陷波频率精确可调性和抽头系数的稀疏性相结合，以达到同时降低FIR多频陷波器设计算法复杂度和硬件实现复杂度的目标。FIR多频陷波器抽头系数的稀疏性，在硬件实现上可大大减少加法器和乘法器数目，从而有效提高其运算速度、减小运算误差，同时降低其功耗和成本。但稀疏FIR滤波器的设计过程通常会涉及复杂的迭代运算和优化过程，具有较高的计算复杂度，而本项目中提出的陷波频率的精确可调性，使得当FIR多频陷波器的陷波频率发生变化时，可以利用已经设计好的稀疏原始滤波器，避免了重新设计整个滤波器，从而有效降低了设计算法的复杂度。本项目的研究对高性能、低功耗的FIR陷波器的设计提供了新的途径和技术参考。

The notch filters that can effectively reject several selected spectral regions while providing high transmission at frequencies outside the rejected regions are widely used in communication systems, radar systems and biomedical signal processing area. In this proposal, the design problems of sparse FIR multiple notch filters with precisely tunable notch frequencies are studied. To reduce the computational complexity and hardware implementation complexity, a novel algorithm is proposed by using a mixture of the precise tuning of frequency properties and the sparsity of the impulse response. The sparse FIR multiple notch filters can significantly reduce the number of the adders and multipliers used in the hardware implementation, the calculation error, and the energy consumption, thus reducing production costs. However，the design of FIR sparse filter always involves iterative procedures and numerical optimization, which results a high computational complexity for the practice system. The precise tuning of frequency properties for the FIR multiple notch filter is a useful operation in the design of digital filters. Instead of designing the filter from scratch, the impulse response of the available filter can be reused. The tuning feature of our scheme reduces the computational complexity of designing the linear phase FIR multiple notch filters. This research has important theoretical and practical value in the implementation of FIR multiple notch filters with high performance and low power consumption。