A General Structure of Linear-Phase FIR Filters with Derivative Constraints

Bo You Yu, Peng Hua Wang, Po-Ning Chen

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, a general structure of linear-phase finite impulse response filters, whose frequency responses satisfy given derivative constraints imposed upon an arbitrary frequency, is proposed. It is comprised of a linear combination of parallelly connected subfilters, called the cardinal filters, with weighted coefficients being the successive derivatives of the desired frequency response at the constrained frequency. An advantage of such a cardinal filters design is that only the weighted coefficients are relevant to the desired frequency response but not the cardinal filters; hence, a dynamic adjustment of the filter system becomes feasible. 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 efficient their computations. At last, a simple enhancement of the cardinal filters design by incorporating the mean square error minimization is presented through examples.

Original languageEnglish
Article number7865939
Pages (from-to)1839-1852
Number of pages14
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number7
StatePublished - Jul 2017


  • Finite impulse response (FIR) filters
  • linear phase filters
  • maximally flat (MF) filters
  • Taylor interpolation
  • FLAT


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