genpark-iir-filter-butterworth-bilinear-transform-skill
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Butterworth Infinite Impulse Response (IIR) digital filter design using Bilinear Transform and s-plane pole mapping
README.md
Butterworth IIR Filter Skill
Second-order maximally flat magnitude low-pass Infinite Impulse Response (IIR) filter designed using the Bilinear Transform.
flowchart TD
Cutoff["Cutoff Frequency Ratio (0..1)"] --> Prewarp["Prewarp Angular Frequency: tan(π f_c / 2)"]
Prewarp --> Bilinear["Bilinear Transform s = 2/T * (z-1)/(z+1)"]
Bilinear --> Coeffs["Difference Equation Direct Form II: y[n] = ∑ b_k x[n-k] - ∑ a_k y[n-k]"]
Coeffs --> Filtered["Low-Pass Clean Output Stream"]
Features
- 100% Python Standard Library: Pure difference equation direct form evaluation.
- Maximally Flat Passband: No passband ripples (unlike Chebyshev or Elliptic filters).
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