Type II, III, and IV Linear-Phase FIR Structures Based on Cardinal Filters

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Novel structures of type II, III, and IV linear-phase finite impulse response (FIR) systems are proposed. It is constituted of a linear combination of basic sub-filters, called cardinal filters, with weighting coefficients equal to the derivatives of the system amplitude response at a prescribed 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. Design examples of maximally flat filters show that further improvement by combining derivative constraints with the least squared error optimization technique can be obtained.

Original languageEnglish
Article number8610214
Pages (from-to)1920-1924
Number of pages5
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number11
StatePublished - Nov 2019


  • derivative constrained filters
  • FIR filters
  • linear-phase filters
  • maximally flat filters


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