Examples
Examples
Try the starting example
- Numerator b coefficients
- 0.5,0.5
- Denominator a coefficients
- 1,-0.3
- Impulse length
- 16
- Impulse response
- [0.5,0.65,0.195,0.0585,0.01755,0.005265,0.0015795,0.00047385,0.000142155,0.0000426465,0.00001279395,0.000003838185,0.0000011514555,3.4543665e-7,1.03630995e-7,3.10892985e-8]
- Cumulative impulse response
- [0.5,1.15,1.345,1.4035,1.42105,1.426315,1.4278945,1.42836835,1.428510505,1.4285531515,1.42856594545,1.42856978364,1.42857093509,1.42857128053,1.42857138416,1.42857141525]
Try another scenario
- Numerator b coefficients
- [0.5, 0.5]
- Denominator a coefficients
- [1, -0.3]
- Impulse length
- 17
- Impulse response
- [0.5,0.65,0.195,0.0585,0.01755,0.005265,0.0015795,0.00047385,0.000142155,0.0000426465,0.00001279395,0.000003838185,0.0000011514555,3.4543665e-7,1.03630995e-7,3.10892985e-8,9.32678955e-9]
- Cumulative impulse response
- [0.5,1.15,1.345,1.4035,1.42105,1.426315,1.4278945,1.42836835,1.428510505,1.4285531515,1.42856594545,1.42856978364,1.42857093509,1.42857128053,1.42857138416,1.42857141525,1.42857142457]
Calculation method
Calculation method
Impulse response
Direct difference equation y[n]=(sum b[k]x[n−k]−sum a[k]y[n−k])/a[0].
Cumulative impulse response
Running sum of impulse response.
Symbols and units
- a
- Numerator b coefficients
- b
- Denominator a coefficients
- c
- Impulse length
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
- Filter coefficients, impulse length. Returns Impulse and cumulative response. 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. Numerator b coefficients: minimum None, maximum 1000000000000.0. Denominator a coefficients: minimum None, maximum 1000000000000.0. Impulse length: minimum 1, maximum 256.
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.