#signal-processing

Chebyshev Type I filter-design maths as an API, computed locally and deterministically. The order endpoint computes the minimum filter order to meet a specification, n = ⌈acosh(√((10^(As/10)−1)/(10^(Ap/10)−1))) / acosh(fs/fp)⌉, from the passband edge frequency and its ripple and the stopband edge and its required attenuation — a Chebyshev filter usually needs a lower order than a Butterworth for the same specification, trading a flat passband for equiripple. The response endpoint computes the equiripple magnitude response, |H| = 1/√(1 + ε²·Tₙ²(f/fc)) with the ripple factor ε = √(10^(Ap/10) − 1) and the Chebyshev polynomial Tₙ, in linear and decibel form — in the passband the magnitude ripples between 0 and −Ap dB and reaches exactly −Ap dB at the cutoff, then rolls off faster than a Butterworth. The ripple endpoint converts between the passband ripple in decibels and the ripple factor ε, with the passband maximum and minimum. Frequencies are in hertz, 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, communications and instrumentation app developers, filter-design and selectivity tools, and signal-processing education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is the Chebyshev Type I filter; for the maximally-flat Butterworth use a Butterworth API.

api.oanor.com/chebyshev-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