Bandwidth Error of Symmetrical Bandpass Filters Used for Analysis of Noise and Vibration

Abstract

The most common device for analyzing sounds is the bandpass litter, usually with a bandwidth of one octave or a fraction there of, e.g., (one-half or one-third. Recently 1/3-octave filters are also being used for vibration analyses. The effective bandwidth of these filters is affected not only by the obvious design parameters of filter cutoff/frequency and the number of resonant elements employed which determines the attenuation rate outside the passband but also on the slope of the noise spectrum which is being analyzed. This paper investigates the effect of all these variables on the effective bandwidth of a symmetrical bandpass filter by means of a normalized mathematical model and expresses the result in terms of bandwidth error. It is found (1) that the bandwidth error increases very rapidly for large values of spectrum slope; (2) that the bandwidth error is symmetrical about an equal energy per octave spectrum slope and that an optimum design point for attenuation at the filter band edges exists for minimizing bandwidth error as a function of spectrum slope.