Calculator Inputs
Choose a mode, enter the required values, and submit to solve the remaining digital cutoff metrics.
Example Data Table
| Case | Mode | fs (Hz) | fc (Hz) | fn | ω (rad/sample) |
|---|---|---|---|---|---|
| Audio low-pass | fs and fc | 48,000 | 5,000 | 0.208333 | 0.654498 |
| Sharper audio edge | fs and fc | 44,100 | 8,000 | 0.362812 | 1.139793 |
| Normalized design target | fs and fn | 96,000 | 12,000 | 0.250000 | 0.785398 |
| Back-solving sampling rate | fc and fn | 50,000 | 2,500 | 0.100000 | 0.314159 |
Formula Used
Nyquist frequency: fN = fs / 2
Normalized cutoff: fn = fc / fN = 2fc / fs
Digital angular frequency: ω = 2πfc / fs = πfn
Cutoff from normalized value: fc = fn × fs / 2
Cutoff from digital angular value: fc = ωfs / 2π
Prewarped analog cutoff for bilinear mapping: Ωc = 2fs tan(ω / 2)
Prewarped analog frequency in hertz: fpre = Ωc / 2π
Equivalent time constant: τ = 1 / Ωc
The standard cutoff point is usually the frequency where the magnitude drops to 0.707 of passband amplitude, which equals about -3.01 dB.
How to Use This Calculator
- Select the calculation mode that matches the values you already know.
- Enter any two required inputs such as fs and fc, or fs and fn.
- Choose a reference response type and filter order for the graph.
- Press Calculate to solve the remaining cutoff relationships.
- Review the result table for Nyquist, normalized, angular, and prewarped values.
- Use the CSV or PDF buttons to export the result summary for documentation.
FAQs
1. What is digital filter cutoff frequency?
It is the reference frequency where a filter begins significant attenuation. In many practical designs, the cutoff is defined at the -3 dB point, where amplitude falls to about 70.7% of passband level.
2. Why is normalized cutoff useful?
Normalized cutoff removes unit dependence and expresses the design relative to the Nyquist frequency. That makes filter specifications portable across different sampling rates and easier to compare during design.
3. What is the valid range for normalized cutoff?
For this definition, normalized cutoff should stay between 0 and 1. A value of 1 means the Nyquist limit, which is not a valid practical cutoff target.
4. Why must cutoff stay below Nyquist?
The Nyquist frequency is half the sampling rate. Frequencies above it fold back by aliasing, so a valid digital cutoff must remain below that boundary for meaningful design.
5. What does prewarped analog cutoff mean?
Prewarping compensates for the nonlinear frequency mapping introduced by the bilinear transform. It helps analog prototype designs land closer to the intended digital cutoff after transformation.
6. Does the graph represent an exact final filter?
No. The graph is a clean reference curve based on the selected order and response type. It is meant for visualization of cutoff behavior, not exact implementation coefficients.
7. When should I use digital angular frequency?
Use digital angular frequency when working directly in radians per sample, especially in DSP equations, z-domain analysis, and coefficient derivations.
8. Can I use this for low-pass and high-pass checks?
Yes. The solved cutoff relationships are the same, while the graph can be shown as either low-pass or high-pass to visualize the expected attenuation trend.