Design IIR Butterworth Filters Using 12 Lines of Code
TimelessIntermediate
While there are plenty of canned functions to design Butterworth IIR filters [1], it's instructive and not that complicated to design them from scratch. You can do it in 12 lines of Matlab code.
Summary
This short article shows how to design Butterworth IIR filters from first principles and implement them in just 12 lines of MATLAB code. Readers will learn the derivation from the analog prototype to a stable digital realization and how to verify the result with basic spectral checks.
Key Takeaways
- Implement a Butterworth IIR filter in MATLAB in 12 concise lines of code.
- Derive analog Butterworth pole locations and convert them to the z-plane.
- Apply the bilinear transform with frequency prewarping to meet digital specs.
- Validate frequency response using FFT-based spectral analysis and plotting.
- Structure the realization (e.g., cascaded biquads) to preserve numerical stability.
Who Should Read This
DSP engineers, researchers, or graduate students with basic filter theory who want a compact, implementation-focused walkthrough of Butterworth IIR design in MATLAB.
TimelessIntermediate
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