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genpark-fast-fourier-transform-radix2-dit-skill

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SUMMARY

Radix-2 Decimation-in-Time (DIT) Fast Fourier Transform (FFT) and Inverse FFT with twiddle factor tables

README.md

Radix-2 Cooley-Tukey Fast Fourier Transform Skill

In-place decimation-in-time (DIT) Fast Fourier Transform with bit-reversal sorting and butterfly twiddle factor recombination.

flowchart LR
    Time["Time Domain Signal x[n]"] --> BitRev["Bit-Reversal Permutation"]
    BitRev --> Butterfly["Log2(N) Butterfly Stages (Twiddle W_N^k)"]
    Butterfly --> Freq["Frequency Spectrum X[k]"]
    Freq --> IFFT["Conjugate Reversal IFFT"]
    IFFT --> Time

Features

  • 100% Python Standard Library: Pure standard complex math.
  • O(N log N) Efficiency: High-performance discrete Fourier transform.
  • Round-Trip Precision: Exact analytical inversion.

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