Digital Filter Designer Calculator

Calculator Inputs

Design Method

Response Type

Sample Rate (Hz)

Cutoff / Edge 1 (Hz)

Cutoff / Edge 2 (Hz)

Transition Width (Hz)

Passband Ripple Target (dB)

Stopband Attenuation Target (dB)

Window Type

Tap Selection

Manual Taps

Q Factor

Coefficient Precision

Graph Scale

FIR mode estimates taps using transition width and selected window. IIR mode builds a biquad using frequency and Q. Band designs use both edge frequencies.

Example Data Table

Scenario	Method	Sample Rate	Response	Main Inputs	Typical Use
Audio cleanup	FIR	48000 Hz	Low-pass	Cutoff 6000, transition 1200, attenuation 60	Reduce high-frequency hiss
Sensor drift removal	IIR	1000 Hz	High-pass	Cutoff 2, Q 0.707	Suppress slow baseline drift
Speech band isolation	FIR	16000 Hz	Band-pass	Edges 300 and 3400, transition 250	Keep speech-rich frequencies
Mains hum rejection	IIR	2000 Hz	Band-stop	Edges 49 and 51, Q auto from band	Reject narrow interference tone

Formula Used

FIR windowed-sinc design: the ideal low-pass kernel is h_d[n] = 2f_c/f_s × sinc((2f_c/f_s)(n-M)), where M = (N-1)/2. High-pass, band-pass, and band-stop responses are built by spectral inversion or subtraction. The final taps are h[n] = h_d[n] × w[n].

Window impact: rectangular gives the sharpest transition with higher ripple. Hann, Hamming, and Blackman trade a wider transition for improved sidelobe suppression and deeper stopband attenuation.

IIR biquad design: the calculator uses standard digital biquad equations with ω₀ = 2πf₀/f_s and α = sin(ω₀)/(2Q). The transfer function is H(z) = (b0 + b1z^-1 + b2z^-2) / (1 + a1z^-1 + a2z^-2).

Key engineering relationships: smaller transition width usually requires more FIR taps. Higher Q narrows the IIR band response or notch. Group delay for linear-phase FIR filters is approximately (N-1)/2 samples.

How to Use This Calculator

Select FIR Windowed-Sinc for linear phase, or IIR Biquad for low computational cost.
Choose the filter response type: low-pass, high-pass, band-pass, or band-stop.
Enter the sample rate. Your cutoff values must remain below half that sample rate.
For FIR mode, set transition width, attenuation target, and either auto or manual taps.
For IIR mode, enter Q. For band filters, provide both edges so the center frequency can be derived.
Click Design Filter to generate coefficients, response plots, and sampled response values.
Use the CSV button for spreadsheet analysis and the PDF button for a portable design report.
Review stability, group delay, and magnitude response before deploying the design in production code or embedded hardware.

FAQs

1. What is the difference between FIR and IIR filters?

FIR filters can provide linear phase and are easier to reason about, but they often need more coefficients. IIR filters reach similar selectivity with fewer coefficients, but phase distortion and stability must be checked carefully.

2. When should I choose a low-pass filter?

Use a low-pass filter when you want to preserve lower frequencies and suppress higher-frequency noise. Common cases include smoothing sensor data, anti-alias filtering, and reducing hiss in sampled audio.

3. Why does transition width matter so much?

Transition width describes how quickly the filter moves from passband to stopband. Narrow transitions demand a steeper response, which usually means more FIR taps or a higher-selectivity IIR configuration.

4. What does Q factor control in IIR mode?

Q sets how sharp the resonance or notch becomes around the reference frequency. Larger Q values produce narrower, more selective band-pass or band-stop responses, while lower Q values make the curve broader.

5. Why are odd tap counts preferred in this FIR calculator?

Odd tap counts place the symmetry center on an actual coefficient. That makes many linear-phase designs, especially low-pass and high-pass filters, easier to construct and interpret consistently.

6. How should I interpret the magnitude plot?

The magnitude plot shows gain versus frequency. In dB scale, 0 dB means near-unity gain. Negative values indicate attenuation, and the steepness around cutoff reflects selectivity.

7. Can I use the coefficients directly in embedded code?

Yes, but verify numeric precision, quantization effects, and runtime limits first. Fixed-point implementations often need scaling, saturation handling, and additional validation against target hardware behavior.

8. Does this calculator replace a full DSP toolchain?

It is a practical design and estimation tool, not a complete verification environment. Final deployment should still include simulation, frequency sweeps, numerical testing, and application-specific validation.