Circuits, Systems, and Signal Processing

, Volume 38, Issue 2, pp 481–497 | Cite as

Optimizing Order to Minimize Low-Pass Filter Lag

  • Fredrik DessenEmail author


This paper develops a tool kit for designing low-pass filters to exhibit the smallest possible phase drop. Based solely on the stopband requirements, it is thus possible to find the best order for a filter to be employed in a feedback loop. That is shown for two much-used filter families, Butterworth and Bessel, in cases where the filter is specified to have a minimum attenuation above a certain frequency. It is argued that the phase drop can be represented by an equivalent filter delay. Design tools are then developed, which do not depend on the precise dynamics of the application process. The tools comprise not only the means for determining the optimal filter order and bandwidth, but also formulae and tables useful for obtaining the resulting filter delay. A simple approximation is subsequently developed, which links the minimum obtainable delay directly to said requirements. The filter order need not be known to apply this expression, and the filter family is represented in it by no more than a single constant. This rule of thumb is finally adapted to the area of anti-aliasing filters and there briefly compared to approximative formulae found in existing literature.


Feedback systems Filter design Low-pass filters Minimum delay Optimal filter order Stopband attenuation 

Supplementary material

34_2018_877_MOESM1_ESM.pdf (285 kb)
Supplementary material 1 (pdf 284 KB)
34_2018_877_MOESM2_ESM.pdf (296 kb)
Supplementary material 2 (pdf 296 KB)


  1. 1.
    A. Antoniou, Digital Signal Processing (McGraw-Hill, New York, 2006)Google Scholar
  2. 2.
    K.J. Åström, B. Wittenmark, Computer-Controlled Systems: Theory and Design (Prentice Hall, New Jersey, 1997)Google Scholar
  3. 3.
    T.F. Bogart, J.S. Beasley, G. Rico, Electronic Devices and Circuits (Prentice Hall, New Jersey, 2001)Google Scholar
  4. 4.
    S. Elliott, Signal Processing for Active Control (Academic Press, London, 2001)Google Scholar
  5. 5.
    S. Franco, Design with Operational Amplifiers and Analog Integrated Circuits (McGraw-Hill, New York, 2002)Google Scholar
  6. 6.
    K. Henderson, W. Kautz, Transient responses of conventional filters. IRE Trans. Circuit Theory 5(4), 333–347 (1958)CrossRefGoogle Scholar
  7. 7.
    L.D. Paarmann, Design and Analysis of Analog Filters: A Signal Processing Perspective (Springer, Berlin, 2001)Google Scholar
  8. 8.
    L. Thede, Practical Analog and Digital Filter Design (Artech House, Norwood, 2004)Google Scholar
  9. 9.
    W. Thomson, Delay networks having maximally flat frequency characteristics. Proc. IEE Part III Radio Commun. Eng. 96(44), 487–490 (1949)CrossRefGoogle Scholar
  10. 10.
    M.E. Van Valkenburg, Analog Filter Design (Holt, Rinehart and Winston, New York, 1982)Google Scholar
  11. 11.
    B. Wittenmark, K.J. Åström, K.E. Årzén, Computer control: an overview (IFAC Prof. Brief, 2002)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of Engineering CyberneticsNorwegian University of Science and Technology (NTNU)TrondheimNorway

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