IIR Filter Calculator Inputs
Example Data Table
| Use Case | Filter Type | Sample Rate (Hz) | Frequency Setting (Hz) | Q Factor | Typical Goal |
|---|---|---|---|---|---|
| Audio noise cleanup | Low-Pass | 48000 | 2000 | 0.707 | Reduce high-frequency noise |
| Sensor drift removal | High-Pass | 1000 | 10 | 0.707 | Remove slow baseline drift |
| Vibration isolation | Band-Pass | 8000 | 400 to 800 | 1.333 | Keep a target resonance band |
| Mains hum suppression | Notch | 2000 | 49 to 51 | 50 | Reject a narrow interference tone |
Formula Used
This calculator uses standard second-order biquad IIR equations. Coefficients are created from digital frequency and Q factor using trigonometric terms. The normalized transfer function is:
H(z) = (b0 + b1z^-1 + b2z^-2) / (1 + a1z^-1 + a2z^-2)
The time-domain implementation uses the recursive difference equation below:
y[n] = b0x[n] + b1x[n−1] + b2x[n−2] − a1y[n−1] − a2y[n−2]
For low-pass and high-pass designs, the key angular frequency is:
ω0 = 2πf0 / fs, α = sin(ω0) / (2Q)
For band-pass and notch filters, the center frequency and bandwidth determine an equivalent Q. Stability is checked by confirming both poles remain inside the unit circle.
How to Use This Calculator
- Select the desired IIR filter type.
- Enter the sample rate used by your digital system.
- Provide the cutoff frequency, or the lower band edge.
- For band-pass or notch, enter the upper band edge too.
- Set the Q factor to control selectivity and sharpness.
- Enter an input amplitude for output magnitude estimation.
- Add frequency points for response analysis.
- Choose impulse response sample length.
- Press the calculate button.
- Review coefficients, poles, tables, and graphs above the form.
- Export your report as CSV or PDF when needed.
FAQs
1. What is an IIR filter?
An IIR filter is a recursive digital filter. It uses current and past inputs plus past outputs. That feedback makes it efficient and powerful for real-time engineering systems.
2. Why does Q factor matter?
Q factor controls how sharp or selective the filter becomes. Higher Q creates a narrower and stronger peak or rejection zone around the target frequency.
3. What does stability mean here?
A stable IIR filter produces bounded output for bounded input. In practice, the poles must stay inside the unit circle in the z-plane.
4. When should I use a low-pass filter?
Use a low-pass filter when you want slow or lower-frequency content and need to remove fast noise, ripple, or unwanted high-frequency components.
5. When should I use a high-pass filter?
Use a high-pass filter to remove DC offset, baseline drift, or very slow changes while keeping more rapidly changing signal content.
6. What is a notch filter used for?
A notch filter removes a very narrow unwanted frequency band. It is useful for suppressing power-line hum, single-tone interference, and fixed resonances.
7. Why are coefficients normalized?
Normalization divides all coefficients by a0 so the denominator starts with one. That form is standard for direct-form digital implementation.
8. Can I use this for embedded systems?
Yes. The displayed coefficients and recursive equation are suitable for firmware, DSP code, simulations, and controller prototypes, provided scaling is handled correctly.