Level 1Edit

Filter notesEdit

These notes were originally made for the filter polynomial article, but some of this material could usefully be added to Analogue filter, Network synthesis filter, Network synthesis (because that article is light on approximation techniques), and/or Filter (signal processing)

Paarmann p.15

Succint summary of early network synthesis filters. Much of this should be in the Analogue filter article history section.

  • Butterworth filter (Butterworth 1930)
  • Elliptical filter (Cauer 1931)
  • Bessel filter (Thomson 1949; Storch, 1954)
  • Chebychev filter (Cauer, 1958) (source conflict - Cauer was dead by this date, presumably this means the date of US publication after the war)
Paarmann p.16
  • Papoulis introduced filters with a maximum magnitude slope at the passband edge for a given monotonic response falloff for a given order (1958) (source conflict - most sources are calling Papoulis' filter the Legendre filter)
  • Halpern extended Papoulis for monotonic band falloff using Jacobi polynomials (1969)
  • Ku and Drubin introduced filters based on Legendre and Hermite polynomials (1962) (source conflict - other sources credit Papoulis with Legendre filters. Later Paarmann has Papoulis' filter as one specific type and others as associate Legendre filters)
  • Scanlan introduced filters with poles lying on an ellipse equally spaced in frequency (1965) The eccentricity of the ellipse trades magnitude response with time-domain response.
  • Johnson and Johnson introduced filters using ultraspherical polynomials (1966). Also showed that Butterworth, Chebychev and Legendre filters were all special cases of these.
  • Attikiouzel and Phuc (1978) - ultraspherical and modified ultraspherical polynomials with a single parameter determining transitional forms.
  • Rabrenovic and Lutovac (1992) - extension to Cauer filters using quasi-elliptical functions and elliptical filters without the need to invoke elliptical functions.
Paarmann p.16 - time-delay filters
  • Bessel filter - maximally flat time-delay
  • Macnee (1963) introduced a filter with a Chebychev approximation to constant time-delay.
  • Bunker (1970) Chebychev polynomials, ripple in time-delay or phase. (How is this different from Macnee's filter?)
  • Ariga and Masamitsu (1970)
  • Halpern (1976) used hyperbolic function approximation to improve low-order Bessel filters.
  • Bennett (1988) introduced hour-glass filter. Has both equiripple time-delay and equiripple magnitude response.
  • Gaussian filters (Dishal 1959) similar to Bessel but with less delay.


  • Paarmann, Larry D., Design and Analysis of Analog Filters, Springer, 2001 ISBN 0792373731.