The Fast Fourier Transform - Most Ingenious Algorithm Ever?

The Fast Fourier Transform - Most Ingenious Algorithm Ever?

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Polynomial Multiplication Flowchart

5 of 12

5 of 12

Polynomial Multiplication Flowchart

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The Fast Fourier Transform - Most Ingenious Algorithm Ever?

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  1. 1 Introduction
  2. 2 Polynomial Multiplication
  3. 3 Polynomial Representation
  4. 4 Value Representation Advantages
  5. 5 Polynomial Multiplication Flowchart
  6. 6 Polynomial Evaluation
  7. 7 Which Evaluation Points?
  8. 8 Why Nth Roots of Unity?
  9. 9 FFT Implementation
  10. 10 Interpolation and Inverse FFT
  11. 11 Recap
  12. 12 Also a subtle mistake that a commenter made me aware of -- at instead of replacing w with 1/n * e^{-2 * pi i/ n}, the actual right way to do this is by taking the final output of the IFFT at the end…

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