Design of FIR digital differentiators using maximal linearity constraints

Ishtiaq Rasool Khan, Masahiro Okuda, Ryoji Ohba

Research output: Contribution to journalJournal articlepeer-review

8 Scopus citations


Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.

Original languageEnglish
Pages (from-to)2010-2017
Number of pages8
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number8
StatePublished - Aug 2004
Externally publishedYes


  • Digital differentiators
  • Digital filters
  • Fullband
  • Maximally linear


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