The Fast Fourier Transform. by Jorge M. Trabal. Outline and Reading. Polynomial Multiplication Problem Primitive Roots of Unity (§10.4.1) The Discrete Fourier Transform (§10.4.2) The FFT Algorithm (§10.4.3) Integer Multiplication (§10.4.4) Java FFT Integer Multiplication (§10.5).
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The Fast Fourier Transform
by
Jorge M. Trabal
FFT
FFT
FFT
FFT
where
FFT
FFT
Set of integers between 1 and n that are relative prime to n.
FFT
The properties are satisfied
n complex roots of unity equally spaced around the circle of unit radius centered at the origin of the complex plane.
FFT
FFT
FFT
FFT
FFT
into two polynomials
and we can write
FFT
FFT
The running time is O(n log n). [inverse FFT is similar]
FFT
FFT
FFT
FFT
FFT
FFT
FFT