First-Order Low-Pass Filter Coefficient (α)
From sample period and cut-off, get the first-order IIR coefficient α, the fixed-point Q coefficient and settling time — ready to paste into ADC smoothing code.
Key points
First-Order Low-Pass Filter Coefficient (α): From sample period and cut-off, get the first-order IIR coefficient α, the fixed-point Q coefficient and settling time — ready to paste into ADC smoothing code. Formula: α = Ts/(RC + Ts), RC = 1/(2πf_c); y += α(x − y). Enter parameters on the DD-CAT IDE online tool page to get results instantly, with a calculation-model diagram that updates with the inputs. The fixed-point form is y = y + ((α_q * (x − y)) >> 16); mind the accumulator width and sign extension. Keep the cut-off well below the sample rate (at least 1/10), otherwise the discrete response drifts from the design.
Inputs
α = Ts/(RC + Ts), RC = 1/(2πf_c); y += α(x − y)Calculation model (updates with parameters)
| Filter coefficient α | 0.385870 | y += α·(x − y) |
| Time constant τ = RC | 15.92 ms | |
| Theoretical cut-off | 10 Hz | 离散实现Actual 7.76 Hz |
| Actual discrete -3dB frequency | 7.76 Hz | |
| Fixed-point coefficient | 25288 | Q16：y += (α_q·(x − y)) >> 16（按所选格式移bits） |
| Settling time (±1%) | 79.58 ms | About 5τ |
| Output one sample after a step | 38.59 % | Measures response speed |
Engineering notes
- The fixed-point form is y = y + ((α_q * (x − y)) >> 16); mind the accumulator width and sign extension.
- Keep the cut-off well below the sample rate (at least 1/10), otherwise the discrete response drifts from the design.
FAQ
- What is First-Order Low-Pass Filter Coefficient (α) for?
- From sample period and cut-off, get the first-order IIR coefficient α, the fixed-point Q coefficient and settling time — ready to paste into ADC smoothing code.
- What is the formula for First-Order Low-Pass Filter Coefficient (α)?
- Core formula: α = Ts/(RC + Ts), RC = 1/(2πf_c); y += α(x − y). The tool returns results instantly using this formula and the selected parameters.
- What engineering notes should I keep in mind when using First-Order Low-Pass Filter Coefficient (α)?
- The fixed-point form is y = y + ((α_q * (x − y)) >> 16); mind the accumulator width and sign extension. Keep the cut-off well below the sample rate (at least 1/10), otherwise the discrete response drifts from the design.