FFT(Fast Fourier Transform). p2. FFT Coefficient representation: How to evaluate A(x 0 )?

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Presentation transcript:

FFT(Fast Fourier Transform)

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

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

p4. Thm1 Pf:

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

p6. Point-value rep. Cof. rep.

p7. Thm2

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

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

p10. DFT

p11. Interpolation at the complex roots of unity:

p12. Thm 7 Pf:

p13. FFT

p14.

p16. Thm 8 (Convolution thm) Componentwise product

Efficient FFT implement

p19.

FFT circuit S=1S=2 S=3