Lecture 10: The Fast Fourier Transform (FFT)
- Complex numbers (see complex.ppt
- Elements of Algebra and Algebraic Computing, John D. Lipson,
Benjamin Cummings Publishing Co., 1981.
- Chapter 9 (pp. 293-308) of Lipson (handout, see above for reference).
- Review of evaluation, pointwise product, interpolation algorithm
for polynomial multiplication.
- Review of matrix interpretation of evaluation and interpolation.
- Horner's method for polynomial evaluation.
- Evaluating a polynomial at a point and its negative.
- Review of complex numbers
- Arithmetic and norm
- Polar coordinates and Euler's identity
- Roots of unity.
- Discrete Fourier Transform as a Vandermonde matrix.
- Evaluating the Vandermonde matrix with even/odd symmetry
- Fast Fourier Transform
- fft.ppt - power point slides containing
lecture notes on the FFT.
Maple worksheets and programs
- interp.mws - Worksheet containing an implementation
of the evaluate, pointwise product, interpolate algorithm for polynomial
- fft.mws - Worksheet containing an implementation
of a recursive FFT.
Created: May 18, 2004 by email@example.com