A general structure of linear-phase FIR filters with derivative constraints

• Main Authors: Yu, Bo-You, 余柏佑
• Other Authors: Chen, Po-Ning
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/8u8ryv

博士 === 國立交通大學 === 電信工程研究所 === 106 === In this dissertation, novel structures of types I, II, III, and IV linear-phase FIR filters, whose frequency responses satisfy given derivative constraints imposed upon an arbitrary frequency, are proposed. It is comprised of a linear combination of parallelly connected sub-filters, called the cardinal filters, with weighted coefficients being the successive derivatives of the desired frequency response at the constrained frequency. Since the cardinal filters can be synthesized via recursive closed-form expressions, regardless of the desired system amplitude response, the proposed structure provides a universal design for arbitrary derivative-constrained linear-phase FIR filters. The key to derive the coefficients of cardinal filters is the determination of the power series expansion of certain trigonometric-related functions. By showing the elaborately chosen trigonometric-related functions satisfy specific differential equations, recursive formulas for the coefficients of cardinal filters are subsequently established, which make stable their computations. At last, a simple enhancement of the cardinal filters design by incorporating the mean square error (MSE) minimization is presented through examples.