基于外插脉冲响应技术的低复杂度FIR滤波器组研究

低（硬件执行）复杂度FIR滤波器组设计是信号处理和通信领域中具有重要理论意义和应用价值的一项研究。已有设计方法在适用范围、滤波器组整体延迟量、信号处理效率和（或）频域选择性能等指标方面存在着局限性。外插脉冲响应（EIR）技术可在基本不影响FIR滤波器其它性能指标的前提下实现其复杂度指标的明显改进，其基本思想是选取合适的列向量对滤波器系数组成的矩阵进行近似。为了完善低复杂度FIR滤波器组设计，本项目首次结合FIR滤波器组的特点和EIR技术的基本思想研究基于EIR技术的低复杂度FIR滤波器组设计。针对一般意义FIR分析滤波器组、两通道正交镜像FIR滤波器组以及多通道余弦调制FIR滤波器组，研究其低复杂度设计，主要包括结构设计和系数优化算法研究。期望所提出设计方案可在基本不影响其它性能指标的前提下实现上述FIR滤波器组复杂度指标的明显改进，且能在包括频谱感知和多载波通信在内的多个领域内得到应用。

Low (hardware implementation) complexity finite impulse response (FIR) filter bank design plays an important role in signal processing and communication with regard to theoretical research and practical application. The existing design methods, however, have several disadvantages with respect to the application range of the methods and/or some performance metrics of the filter bank, such as the delay, the efficiency of signal processing and the frequency selectivity. The extrapolated impulse response (EIR) technique can synthesize an FIR filter with significantly reduced complexity and have little effect on the other performance metrics. Its basic idea is to choose appropriate column vectors to approximate the matrix formed by the filter coefficients. For overcoming the disadvantages of the existing low-complexity FIR filter bank design methods, a novel low-complexity FIR filter bank design scheme is proposed, by exploiting the basic idea of the EIR technique and some properties of the FIR filter bank, in this proposal. In the proposal, the design of the generic FIR analysis filter bank, the two-channel quadrature-mirror FIR filter bank and the cosine modulated FIR filter bank will be studied by using the proposed low-complexity design scheme. The study will include the structure design and the coefficients optimization of the filter bank. It is expected the proposed low-complexity design scheme can synthesize the FIR filter banks mentioned above with obviously improved complexity metric and will have little effect on the other performance metrics, compared to the traditional FIR filter bank design scheme. Further, the proposed low-complexity FIR filter bank is expected to be applicable in various areas, especially in the frequency spectrum sensing and multi-carrier communication.