Why it matters
FFT is one of most important algorithms. Understanding shapes broad application.
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The architecture
Bit-reverse input.
Iterative butterfly.
Roots of unity: exp(2*pi*i/n).
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How it works end to end
Iterative: outer loop over stages (1 to log n).
Inner: butterfly pairs.
Twiddle: precompute.
Inverse FFT: conjugate + divide by n.