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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
Article
  • 155 Downloads

Abstract

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.

Keywords

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)

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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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