Octave Band Pole Calculator
Calculate analog Butterworth bandpass poles for octave and third-octave bands using standard center frequencies.
Author: Third Octave Editorial Team
Technical scope: Preferred center frequencies, analog Butterworth prototype poles, and octave-band transform math used in octave and third-octave filter design.
Reviewed March 2026. These guides are written from an acoustics software and DSP implementation perspective. For regulated or contractual work, check the purchased standard and your instrument documentation directly.
How bandpass poles are formed
Start with low-pass Butterworth prototype poles in the left half-plane. Apply the bandpass transform
s -> (s^2 + w0^2) / (B s) where w0 = sqrt(w1 * w2) and B = w2 - w1.
Each prototype pole produces two bandpass poles.
Choose the band type first, then a standard center frequency to see the resulting analog poles.
Pole calculator (analog)
Poles are shown in rad/s. Digital pole locations depend on the bilinear transform and sample rate.