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FFT(Fast Fourier Transform). FFT. Coefficient representation: . How to evaluate A(x 0 )?. Horner’s rule: Point-value representation:. Thm1. Pf:. n-point interpolation: Lagrange’s formula:. Cof. rep. Point-value rep. Thm2. Lemma 3 (Cancellation Lemma)
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FFT • Coefficient representation: How to evaluate A(x0)?
Horner’s rule: • Point-value representation:
Thm1 Pf:
n-point interpolation: Lagrange’s formula:
Cof. rep. Point-value rep.
Lemma 3 (Cancellation Lemma) n, k, d: non-negative integers, • Cor. 4 n: even positive integer Pf:
Lemma 5 (Halving lemma) Pf: • Lemma 6 (Summation lemma) Pf:
Thm 7 Pf:
Thm 8 (Convolution thm) Componentwise product
FFT circuit S=1 S=2 S=3