John explained to me that his generic PEQ type in REW used RBJ's definition of Q. A recent discussion with John Mulcahy, the author of the Room EQ Wizard (REW) measurement software, brought the actual facts of the matter to light. A casual inspection of these formulas gives the impression that the resulting formula for the bandwidth in Hz might be very messy. When subtracted, his formulas for the half-gain points give the bandwidth in Hz. RBJ computes the upper and lower half-gain points and expresses their ratio in octaves, deriving other useful relationships that I won't discuss here. For example, for a PEQ with a maximum cut of 2 dB, the "half-gain bandwidth" would be calculated by finding the two frequencies for which the cut is 1 dB. In this definition, the upper and lower frequency points for computing bandwidth are found as the frequencies for which the boost (or cut) in dB is one-half the maximum boost (or cut) in dB. To solve this problem, RBJ settles on the "half-gain bandwidth". But since a PEQ filter might have a boost or cut less than 3 dB, such a definition would make no sense. In traditional low-pass and bandpass filters, the -3 dB point is usually the reference for computing bandwidth. In his PDF about PEQ filters, RBJ discusses the definition of bandwidth. Parametric Equalizer " Q" Definitions and Bandwidth (page 2) Calculating the Bandwidth of the Parametric Equalizer Parametric Equalizer Bandwidth Calculations
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