Butterworth Filter API
Butterworth-filter design maths as an API, computed locally and deterministically. The order endpoint computes the minimum filter order needed to meet a specification — from the passband edge frequency and its allowed ripple and the stopband edge frequency and its required attenuation it returns the exact and rounded-up order, n = ⌈log10((10^(As/10)−1)/(10^(Ap/10)−1)) / (2·log10(fs/fp))⌉, where each extra order adds 20 dB per decade of roll-off. The response endpoint computes the maximally-flat magnitude response of an n-th order Butterworth filter at a frequency, |H| = 1/√(1 + (f/fc)^(2n)), in linear and decibel form with the attenuation and the asymptotic roll-off — the response is exactly −3.01 dB at the cutoff for any order. The poles endpoint gives the s-plane pole locations, equally spaced on a circle of radius ωc in the left half-plane at angles π·(2k+n−1)/(2n), all stable. Frequencies are in hertz (or any consistent unit), ripple and attenuation in decibels and the order a positive integer. Everything is computed locally and deterministically, so it is instant and private. Ideal for DSP, audio, RF, instrumentation and embedded app developers, anti-aliasing and filter-design tools, and signal-processing education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the Butterworth filter; for a single-pole RC cutoff and resonance use a resonance API and for AC impedance an impedance API.
api.oanor.com/butterworth-api
