可变带宽FIR数字滤波器的高效加权最小二乘设计及实现

本文提出一种具有稳定相频响应的可变带宽FIR数字滤波器的高效加权最小二乘设计方法.文中将可变带宽FIR数字滤波器的冲击响应表示成以谱参数为变量的基函数的线性组合,进而利用定系数子滤波器的线性组合来实现,这里可变带宽特性直接由可变谱参数所决定.该方法通过建立加权最小二乘目标函数,简单高效地推导出滤波器系数的优化封闭解表达式,复杂度和计算量大大降低.应用这种滤波器的优点在于只有一个直接决定带宽的可调谱参数,更新机制简单.设计实例证明了该方法的高效性和可变带宽滤波器的有效性.

Efficient weighted-least-square design and realization of FIR digital filters with variable bandwidth

This paper proposes an efficient weighted-least-square design method for FIR digital filters with variable bandwidth and stable phase response. The impulse response of the variable-bandwidth FIR digital filter is parameterized as a linear combination of the basic functions with spectral parameters as the varibles. Such filters are implemented as a linear combination of fixed-coefficient subfihers and the variable-bandwidth characteristics are directly determined by tuning spectral parameters. Using the weighted-least-square objective function, the closed-form expressions of optimal solutions are obtained efficiently by solving a group of linear equations. Consequently, a significant reduction in complexity and computational cost can be achieved. The filters are implemented with the aids of only one variable spectral parameter that determines the bandwidth, and a simple update routine. Design examples are provided to demonstrate the effectiveness of the proposed method and the validity of the variable-bandwidth FIR filters.