基于PSWF窗的线性相位FIR-BSF设计

Design of Linear Phase FIR-BSF Based on PSWF Window

针对基于椭圆球面波函数(PSWF)的带阻滤波器(BSF)设计方案研究空白,为发挥PSWF的优势、提升有限脉冲响应(FIR)数字滤波器性能,采用由Hermite函数逼近法得到的PSWF显式渐近表达式产生第0阶PSWF脉冲信号。在此基础上,与其他主流窗函数进行对比,验证了第0阶PSWF窗的最佳时频能量聚集性。同时,给出了基于PSWF窗的线性相位FIR-BSF设计方案与评价指标,并从3个方面进行了数值分析。结果表明:①与其他主流窗函数相比,采用第0阶PSWF窗设计BSF可以使得其阻带衰减至少下降15dB,过渡带宽、通带内衰减、通带波纹等性能指标有不同程度的提升;②通过对相关参数(时间带宽积、窗口长度)变化规律的数值分析可知,PSWF的时间带宽积可控性能够为FIR数字滤波器设计提供更强的灵活性。

Aiming at the research gap for the design of the band-stop filter (BSF) based on the prolate spheroidal wave functions (PSWF),in order to take the advantage of PSWF and improve the performance of the finite impulse response (FIR) digital filter,the PSWF explicit asymptotic expression obtained by Hermite function is used to generate the 0th order PSWF pulse signal.On this basis,compared with other mainstream window functions,the optimal time-frequency energy aggregation of the 0th-order PSWF window is verified.At the same time,the design scheme and evaluation index of linear phase FIR-BSF based on PSWF are given,and the numerical analysis is carried out from three aspects.The results show that:① Compared with other mainstream window functions,using the 0th-order PSWF window to design the BSF can reduce the stopband attenuation by at least 15dB,and the performance indexes such as transition bandwidth,passband attenuation,and passband ripple are also improved to different degrees;② The results of numerical analysis of the variation of related parameters (time bandwidth product,window length) show that PSWF's time-bandwidth product controllability can provide greater flexibility for FIR digital filter design.