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genpark-iir-filter-butterworth-bilinear-transform-skill

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Guvenlik Denetimi
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SUMMARY

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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