filt3dB2QBW

Compute Q and bandwidth of a bandpass filter given its -3 dB points.

When designing an audio bandpass filter, sometimes the -3 dB points f1 and f2 are specified, together with the center frequency f0. These three parameters can be used to compute the Q (quality factor), bandwidth in octaves BWoct, and bandwith BW in frequency units for the bandpass filter in question. The output value ratiof is described below.

Syntax

[Q, BWoct, BW, ratiof] = filt3dB2QBW(f0,f1,f2)

filt3dB2QBW()

The input values of f0, f1, and f2 may be either scalars or a self-consistent set of row or column vectors. If it includes one of the latter, then the output will be the appropriate vector.

Invoking filt3dB2QBW() with no input arguments creates an example table of output results, which can be compared to the results that were published by Bohn (1983).

The mathematical theory that was used by Bohn assumes that f0 is the geometric mean of the two skirt frequencies, f1 and f2, such that f0 = sqrt(f1*f2). However, this is not enforced here in order to allow the function to be used even when dealing with data that may contain measurement errors. An example of such data might arise when reading points from a plotted transfer function response curve.

If the computed value of ratiof = f0/sqrt(f1*f2) is close to unity, then this serves to indicate that the values of f0, f1, and f2 are consistent with the theoretical derivation used here.

Reference

Bohn, Dennis (1983). Bandpass filter design. Studio Sound, January, pages 36-37. https://worldradiohistory.com/Archive-All-Audio/Archive-Studio-Sound/80s/Studio-Sound-1983-01.pdf