1. FFT(Fast Fourier Transform)

2. p2. FFT Coefficient representation: How to evaluate A(x 0 )?

3. p3. Horner’s rule: Point-value representation:

4. p4. Thm1 Pf:

5. p5. n-point interpolation: Lagrange’s formula:

6. p6. Point-value rep. Cof. rep.

7. p7. Thm2

8. p8. Lemma 3 (Cancellation Lemma) n, k, d: non-negative integers, Cor. 4 n: even positive integer Pf:

9. p9. Lemma 5 (Halving lemma) Pf: Lemma 6 (Summation lemma) Pf:

10. p10. DFT

11. p11. Interpolation at the complex roots of unity:

12. p12. Thm 7 Pf:

13. p13. FFT

14. p14.

16. p16. Thm 8 (Convolution thm) Componentwise product

17. Efficient FFT implement

19. p19.

20. FFT circuit S=1S=2 S=3