基于全相位滤波的卷积窗设计

理论推导出全相位数字滤波器的频率采样定理，并证明了无窗、单窗条件下系统特性通过频率采样点而双窗条件下则低于采样点的结论。基于矩形窗、Bartlett、Cosine、Hanning、Hamming、Blackman和Papoulis，分别给出全相位单窗和双窗下卷积窗的过渡带宽度、最小旁瓣衰减及旁瓣衰减速度。在此基础上，本文提出了按照最小二乘准则的窗函数构造的新方法，理论推导出窗函数的算术表达式。实验中，基于全相位数字滤波器幅频特性函数，采用最小二乘法设计最小误差的基窗，与Bartlett基窗相比，误差降低2%且过渡带减少6.9dB。 

Design of Convolution Window Based on All-phase Filtering

The frequency sampling theorem of the full-phase digital filter is derived theoretically, and the conclusion that the system characteristics pass through the frequency sampling point and the double window conditions are lower than the sampling point is proved. Based on rectangular Windows, Bartlett, Cosine, Hanning, Hamming, Blackman, and Papoulis, the transition band widths, minimum side lobe attenuation, and side lobe attenuation speeds of full-phase single and double window convolution windows are given. On this basis, this paper proposes a new method to construct the window function according to the least squares criterion, and theoretically deduces the arithmetic expression of the window function. In the experiment, on the amplitude frequency characteristic function of the full-phase digital filter, the minimum error base window is designed by the least square method. Compared with the Bartlett base window, the error is reduced by 2 % and the transition band is reduced by 6.9 dB.