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The statistical bandwidth of Butterworth filters

Authors
Journal
Journal of Sound and Vibration
0022-460X
Publisher
Elsevier
Publication Date
Volume
115
Issue
3
Identifiers
DOI: 10.1016/0022-460x(87)90295-1
Disciplines
  • Musicology
  • Physics

Abstract

Abstract The precision of standard architectural acoustic measurements is a function of the statistical bandwidth of the band pass filters used in the measurements. The International and United States Standards on octave and fractional octave-band filters which specify the band pass filters used in architectural acoustics measurements give the effective bandwidth, but unfortunately not the statistical bandwidth of the filters. Both these Standards are currently being revised and both revisions require the use of Butterworth filter characteristics. In this paper it is shown theoretically that the ratio of statistical bandwidth to effective bandwidth for an nth order Butterworth band pass filter is 2n (2n−1) . This is verified experimentally for third-octave third-order Butterworth band pass filters. It is also shown experimentally that this formula is approximately correct for some non-Butterworth third-octave third-order band pass filters. Because of the importance of Butterworth filters in the revised Standards, the theory of Butterworth filters is reviewed and the formulae for Butterworth filters given in both revised Standards are derived.

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