用傅立叶级数展开式研究了巴特沃斯型FIR半带低通数字滤波器系数和通用带通数字滤波器系数之间的联系,将其应用于巴特沃斯型FIR带通/带阻和低通/高通数字滤波器的设计,给出了滤波器系数的明晰公式。所设计的数字滤波器以幅度频率响应的平滑度为代价,减小了过渡带宽,具有与切比雪夫型FIR数字滤波器相比拟的性能指标。 The relation between the Butterworth type FIR half-band low-pass digital filter coefficients and the general band-pass digital filter coefficients was studied by Fourier Series Expansion. This method was applied to the Butterworth-type FIR bandpass / band-stop and low- Pass / Qualcomm digital filter design, gives a clear formula of the filter coefficient. The designed digital filter reduces the transition bandwidth at the cost of the smoothness of the amplitude frequency response, and has the performance index compared with the Chebyshev FIR digital filter.