Examples
Examples
Try the starting example
- Butterworth order
- 3
- Digital cutoff frequency (Hz)
- 10
- Sampling rate (Hz)
- 100
- Filter type: 0 lowpass; 1 highpass
- 0
- Numerator coefficients b
- [0.0180989330075,0.0542967990225,0.0542967990225,0.0180989330075]
- Denominator coefficients a
- [1,-1.76004188034,1.18289326204,-0.278059917635]
- Frequency-magnitude pairs
- [[0,1],[1.5625,0.999994026576],[3.125,0.999612339875],[4.6875,0.995503691037],[6.25,0.974675614038],[7.8125,0.909120838739],[9.375,0.775640241642],[10.9375,0.599403142243],[12.5,0.434688288611],[14.0625,0.308416137286],[15.625,0.219163809487],[17.1875,0.157320767852],[18.75,0.114234694954],[20.3125,0.0837915414423],[21.875,0.0619403670491],[23.4375,0.046023953039],[25,0.0342825212814],[26.5625,0.0255311438204],[28.125,0.0189570037298],[29.6875,0.0139921212959],[31.25,0.0102325326409],[32.8125,0.00738611977068],[34.375,0.00523832488334],[35.9375,0.00362920624023],[37.5,0.00243780952237],[39.0625,0.00157133730592],[40.625,0.000957515185832],[42.1875,0.00053911748776],[43.75,0.000269968726877],[45.3125,0.000111961238685],[46.875,0.0000327735202474],[48.4375,0.00000406710012448],[50,0]]
Try another scenario
- Butterworth order
- 4
- Digital cutoff frequency (Hz)
- 10
- Sampling rate (Hz)
- 100
- Filter type: 0 lowpass; 1 highpass
- 0
- Numerator coefficients b
- [0.00482434335772,0.0192973734309,0.0289460601463,0.0192973734309,0.00482434335772]
- Denominator coefficients a
- [1,-2.36951300718,2.31398841442,-1.05466540588,0.187379492368]
- Frequency-magnitude pairs
- [[0,1],[1.5625,0.999999863443],[3.125,0.999964361035],[4.6875,0.999057850502],[6.25,0.990279524603],[7.8125,0.942909948547],[9.375,0.796270064538],[10.9375,0.562315438845],[12.5,0.354092141623],[14.0625,0.217407627872],[15.625,0.135290022505],[17.1875,0.0860380640261],[18.75,0.0558284975925],[20.3125,0.0368139466287],[21.875,0.0245629351649],[23.4375,0.0165145442577],[25,0.0111449257836],[26.5625,0.0075209067043],[28.125,0.0050558181323],[29.6875,0.00337208853616],[31.25,0.00222163868881],[32.8125,0.00143847993137],[34.375,0.00090976872943],[35.9375,0.000557723928575],[37.5,0.000328096342789],[39.0625,0.000182680953421],[40.625,0.0000943759111278],[42.1875,0.0000438777796868],[43.75,0.0000174482268504],[45.3125,0.00000539622765289],[46.875,0.00000104881153792],[48.4375,6.49201954655e-8],[50,0]]
Calculation method
Calculation method
Numerator coefficients b
Bilinear-transform Butterworth poles and zeros; normalize DC or Nyquist gain.
Denominator coefficients a
Real polynomial of digital poles.
Frequency-magnitude pairs
33 points from DC to Nyquist.
Symbols and units
- a
- Butterworth order
- b
- Digital cutoff frequency (Hz)
- c
- Sampling rate (Hz)
- d
- Filter type: 0 lowpass; 1 highpass
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Order, cutoff, sampling rate, filter type. Returns Coefficients and response for review. All coefficients and observations are user supplied; results describe only the stated mathematical model. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification. Butterworth order: minimum 1, maximum 8. Digital cutoff frequency (Hz): minimum 1e-12, maximum 1000000000000.0. Sampling rate (Hz): minimum 1e-12, maximum 1000000000000.0. Filter type: 0 lowpass; 1 highpass: minimum 0, maximum 1.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.