Filter Design Calculator

Design a practical biquad-style lowpass, highpass, bandpass, or notch filter and return coefficients plus response samples.

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What This Calculator Does

This calculator designs a practical second-order digital filter section and extends it into a higher-order cascade when requested. It returns normalized coefficients, pole-zero data, and a sampled magnitude response suitable for MCP or UI rendering.

It combines Filter Type, Filter Family, Order, Sample Rate to estimate B Coefficients, A Coefficients, Cascade Stages.

Formula & Method

A digital biquad uses

H(z)=\frac{b_0+b_1 z^{-1}+b_2 z^{-2}}{1+a_1 z^{-1}+a_2 z^{-2}}

. Lowpass and highpass sections are derived from a center frequency

\omega_0=2\pi f_c/f_s

with family-dependent damping or quality factor.

Notation used in the formulas: $R$ = B Coefficients; $x_{1}$ = Filter Type; $x_{2}$ = Filter Family; $x_{3}$ = Order; $x_{4}$ = Sample Rate; $x_{5}$ = Cutoff / Center Frequency; $x_{6}$ = Bandwidth (Band Filters).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use it when you need practical implementation coefficients and a quick sense of the resulting response without opening a dedicated DSP tool.

Reference Book

Signals and Systems

Alan V. Oppenheim, Alan S. Willsky, and S. Hamid Nawab · Pearson

A classic reference for convolution, Fourier analysis, Laplace transforms, z-transforms, sampling, and LTI systems.

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Inputs Used

Filter Type: Used directly in the calculation.
Filter Family: Used directly in the calculation.
Order: Used directly in the calculation.
Sample Rate: Used directly in the calculation.
Cutoff / Center Frequency: Used directly in the calculation.
Bandwidth (Band Filters): Used directly in the calculation.

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