分数抽样率变换中线性相位FIR滤波器多相分解的对称性研究

Polyphase Decomposition Symmetry Exploitation of Linear Phase FIR Filters for Fractional Sampling Rate Conversion

为提高分数抽样率变换系统的计算效率,在讨论其滤波器多相分解结构的基础上,利用线性相位FIR滤波器的系数对称性,构造多相分解系数的中心对称矩阵,推导出适用于任意分数抽样率和任意滤波器阶数的高效实现方法,并给出所需乘法与加法运算量的计算公式.测试结果表明,与直接计算相比,采用本文方法可减少50%乘法运算和30%加法运算,计算效率显著提高.

In order to improve the computing efficiency of fractional sampling rate conversion, the centrosymmetric matrix of filter polyphase decomposition coefficients is constructed based on the symmetric FIR filter and its polyphase decomposition structure. Then, an efficient implementation applicable to arbitrary fractional sampling rate and filters length is presented. Moreover, the formulation of multiplicative and additive complexity is deduced. The test results show that the proposed method can reduce the number of multiplications by 50 % and number of additions by 30 %, compared with a direct implementation.