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Chapter 2 Discrete Fourier transform

By Happily Fourier Sums

Abstract

as 2 6 6 6 4 B 0 B 1 B 2 B 3 3 7 7 7 5 = 2 6 6 6 4 1 1 1 1 1 W W 2 W 3 1 W 2 W 4 W 6 1 W 3 W 6 W 9 3 7 7 7 5 2 6 6 6 4 b 0 b 1 b 2 b 3 3 7 7 7 5 (2.3) 23 24 CHAPTER 2. DISCRETE FOURIER TRANSFORM Observe that the top row of the matrix evaluates the polynomial at Z = 1, a point where also # = 0. The second row evaluates B 1 = B(Z = W = e i# 0 ), where # 0 is some base frequency. The third row evaluates the Fourier transform for 2# 0 , and the bottom row for 3# 0 . The matrix could have more than four rows for more frequencies and mo

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