Chebyshev Filter API
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
