改进的FIR滤波器结构及性能分析

Improved FIR filter structure with performance analysis

针对数字滤波器在实际应用中的有限字长效应问题,改善有限冲激响应(FIR)滤波器的舍入噪声性能,基于滤波器结构提出一种改进的FIR滤波器结构.给出改进结构的状态空间实现,分析结构参数引入的舍入噪声,并在统计独立的高斯白噪声模型基础上推导出舍入噪声增益表达式.从复杂度、舍入噪声及幅频相频响应方面进行理论推导和仿真验证,性能分析结果表明:改进的结构以复杂度为代价得到舍入噪声增益减小,且在高通和带通滤波器中的舍入噪声性能明显优于其他结构;在不同字长约束下,改进结构的低通、高通及带通滤波器的幅频和相频响应接近理想频响特性.

Aiming at the problem of the finite word length effects of digital filters in practical applications,an improved structure of finite impulse response(FIR) filter was proposed to improve roundoff noise performance of the FIR filter based on filter structure.The state space realization of the improved structure was given,and the roundoff noise introduced by the structural parameters was analyzed.The roundoff noise gain expression was deduced based on the statistical independent Gauss white noise model.The theoretical derivation or simulation verification was carried out from the aspects of complexity,roundoff noise and amplitude-frequency phase-frequency response.The performance analysis results show that the roundoff noise gain of improved structure decreases at the cost of complexity,and the roundoff noise performance is better than other structures in highpass and bandpass filters;the amplitude-frequency and phase-frequency responses of lowpass,highpass and bandpass filters of the improved structure are close to ideal frequency response characteristics under different word length constraints.