基于切比雪夫多项式的函数作为FIR滤波器设计中sinc函数的替代方案
信号处理
2024-07-16 v4
摘要
sinc函数常被用作离散线性相位FIR滤波器设计的基础。然而，截断sinc函数的傅里叶变换由于吉布斯现象在通带内出现波纹。本文引入一种基于切比雪夫多项式的替代函数，其傅里叶变换在通带内单调递减。此外，该函数具有一种内禀窗函数，其可调参数影响过渡带与阻带中的傅里叶变换。
引用
@article{arxiv.2011.10546,
title = {A Function Based on Chebyshev Polynomials as an Alternative to the Sinc Function in FIR Filter Design},
author = {Paul W. Oxby},
journal= {arXiv preprint arXiv:2011.10546},
year = {2024}
}
备注
28 pages, 6 figures, 10 tables. This revision retracts the erroneous last two paragraphs of Section 8. A detailed discussion of the anomalous result illustrated in Figure 6.3 is presented in Appendix 3. The proof of the convergence of the sinc function and the alternative to the sinc function in Section 2 has been replaced with a simpler proof