基于椭圆球面波函数的数字带通滤波器设计

为设计频谱性能优良的有限冲激响应( FIR)数字带通滤波器，从窗函数的性质及选择指标出发，分析了椭圆球面波函数( PSWF)作为窗函数的优势；在此基础上根据数字滤波器设计的原理和要求，选择0阶基带椭圆球面波函数作为窗函数设计数字带通滤波器，并利用微分方程状态转移矩阵逼近的PSWF求解算法，给出了基于PSWF的FIR数字带通滤波器设计方法。理论分析和仿真结果表明：PSWF数字带通滤波器具有较低的设计复杂度，与Kaiser滤波器和Blackman滤波器相比，其旁瓣衰减有超过7 dB的优势，且具有与两种滤波器相当的通带波纹波动和过渡带宽。

Design of digital bandpass filters based on prolate spheroidal wave function

In order to design Finite Impulse Response(FIR) digital bandpass filters with excellent frequency spectrum,the superiority of prolate spheroidal wave functions(PSWF) to window function is analyzed according to the properties and indexes of window function,PSWFs are solved based on state transition matrix approximation,and zero-order baseband is used as window function. On this basis,a method for designing digital bandpass filter based on PSWF is presented. Theoretical analysis and simulation show that PSWF digital filter of bandpass possesses low design complexities,and it owns superiority more than 7 dB in sidelobe fading compared with Kaiser filter and Blackman filter,while the passband ripple and transition band are equal.