任意正交变换下的全相位等效FIR滤波器的构造

为减小正交变换滤波法的计算量并扩大滤波范围，将全相位数字滤波概念推广到任意正交变换．在引入重叠基矩阵的基础上，提出了加窗全相位等效FIR滤波器系数向量的计算通式．严格推导出常用的离散傅里叶变换、离散余弦变换和离散沃尔什变换下的全相位FIR滤波系数的具体表达式．仿真实验表明，全相位滤波可消除截断误差，基于正反变换的N阶全相位滤波结构与长为2N-1的全相位等效FIR滤波器完全等价．

Construction of All-Phase Equivalent FIR Filter Under Arbitrary Orthogonal Transform

To reduce the computation complexity of orthogonal transform filtering method and expand the filtering range, the concept of all-phase digital filtering is extended to the field of arbitrary orthogonal transforms. Based on introducing overlapping base matrix, the general calculating formula for the coefficient vector of windowed all-phase equivalent FIR filter is proposed. Moreover, the concrete expressions for all-phase FIR filtering coefficients under some commonly-used orthogonal transforms including DFT, discrete cosine transform and discrete Walsh transform are strictly deduced. Simulation experiments show that all-phase filtering can eliminate truncation error and the structure of N-order all-phase filtering based on transform and inverse transform is equivalent to all-phase FIR filter with 2N- 1 in length.