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)=rac{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=2pi 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.

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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