模拟／数字混合滤波器组的局部子带重构算法设计

摘要

模拟／数字混合滤波器组（ HFB）系统可以用于实现超宽带模拟信号的高速高精度采样。针对许多应用场合仅需用HFB系统重构特定频带范围内信号的问题，提出通过最小化系统Chebyshev范数设计有限长脉冲响应数字综合滤波器的优化方法。该方法将HFB误差系统转化为一个等价的有限维多输入多输出线性时不变数字系统；在期望重构的频率范围内，利用广义KYP引理，给出数字系统在Chebyshev范数性能指标下基于线性矩阵不等式描述的凸优化问题。该算法可以重构期望的频率范围内的信号。仿真实验表明，新方法设计的HFB重构信号误差小于传统算法设计系统的重构信号误差。%Hybrid filter bank (HFB) analog-to-digital systems permit wideband,high frequency analog-to-digital conversion.To reconstruct the signal of interest in reduced frequency band using HFB,Chebyshev norm performance measure is presented to design finite impulse response (FIR) digital synthesis filters of HFB.The FIR filters are designed to minimize performance measure of a hybrid error system.This hybrid and multirate problem is cast as a norm optimization problem involving only linear time-invariant,discrete-time system.Using the generalized Kalman-Yakubovich-Popov (KYP) lemma,the problem is reduced to an optimization problem with a linear matrix inequality.Numerical experiments show the proposed approach yields better performance compared to existing techniques.