全相位自适应滤波器设计

Design of Adaptive All-phase Filter

文中首先通过单位圆相位影射的方式推导出任意正交变换下全相位信号处理的数学表达式,并画出系统实现原理图和带双窗的全相位正交变换域处理图。基于全相位数字滤波器,本文设计并实现了频域自适应滤波器,对加噪信号进行N次全相位频谱归一化处理,并递归设置幅值为1的频点而形成完整的传输特性,噪声的判断通过单次谱分析和全相位谱分析的均值和方差特性来进行。实验中,对于淹没在强噪声中的信号进行了全相位自适应滤波,结果表明,对于整倍频率分辨率信号可以无失真恢复。全相位自适应滤波恢复得到的信号信噪比提高0.8dB左右,而且通过提高滤波器阶数N或进行频谱校正可以进一步提高恢复信号质量。

In this paper all-phase signal processing mathematical expression is firstly deduced by means of mapping the phase in unit circle to all-phase outputs and the implementation system is also given.The reason of improving all-phase processing effect by adding windows is pointed out.Accordingly the architecture of all-phase with dual-window in orthogonal transform is drawn out.Secondly,adaptive filter based on all-phase is designed,in which signals adding noise are processed N times in the all-phase spectrum normalization way.It is recursively to set frequency point to amplitude 1 so to form the whole transmission property H.Noise is judged by the mean value and variance of single and all-phase spectrum analysis.In the test,the drowned signals by noise are processed using all-phase adaptive filter.The result verifies that signals which frequency is n times of spectrum resolution can be totally recovered without lost.Signal quality is improved by 0.8dB,which can be further improved by means of increasing N or correcting spectrum.