摘要
本文提出了一种新型的全相位DFT数字滤波器频率响应的求取方法—循环移位图法,它是基于全相位滤波器和原有FIR滤波器的相互关系而构造的,充分体现了Fourier变换的循环移位性质和卷积窗的关系。该方法直观,深刻反映了全相位滤波器的内在机理。文中以N=3为例,说明了全相位滤波器的衍生过程。并以N=7阶全相位滤波器为例,分别在无窗、单窗和双窗条件下,推导出了全相位滤波器频率响应的数学表达式,并且用该表达式结合实验结果解释了全相位滤波器的优良特性。然后分别用所有数字角频率的正弦信号对全相位数字滤波器进行仿真实验测试,该仿真实验证明:测试出的频率响应曲线和理论推导完全一致。本文最后还推导出任意阶、任意种加窗方式下的全相位数字滤波器的频率响应公式。
This paper presents a novel solution to acquire the frequency response of all-phase DFT digital filter-cycle shift figure method, which is constructed based on the relation between all-phase filter and the original FIR filter. It embodies the connection between DFT＇ s character of cycle shift and convolution window. Moreover this method is intuitionistic to reflect the mechanism of all phase filter. This paper takes 3-order filter as an example to explain all-phase filter＇s deriving process. In addition, the frequency response＇ s mathematic expression for 7-order all-phase filter, which can interpret all-phase filter＇ s excellent traits combining with experimental results, is deduced successfully on the condition of no-window, single-window and dual-window. To verify these expressions, the sine signals with all the digital circular frequencies are fed to all-phase filter to test the output. This test proves that the curve of allphase filter＇ s frequency response is entirely consistent with the theoretical deduction. As a summary, the frequency response expression for the all-phase filter with any order and with any kinds of window added is given.
出处
《信号处理》
CSCD
北大核心
2007年第4期531-535,共5页
Journal of Signal Processing
关键词
全相位DFT数字滤波器
循环移位图
频率响应
卷积窗
all-phase DFT digital filter
cycle shift figure
frequency response
convolution window
