Lecture 3: Numeric Recipes vs. FFTW
Background Material
- FFT
- Recurrence relations, Catalan Numbers, and Stirling's Formula
- Matrix Notation and Manipulation
Reading
- J. M. Cooley and J. W. Tukey, "An algorithm for the machine
calculation of complex Fourier series", Math. Comp., Vol. 19, 1965,
pp. 297-301.
- M. Frigo and S. Johnson, "The Design and Implementation of FFTW3",
Proc. IEEE, Vol. 93, No. 2, 2005, pp. 216-231.
- M. Frigo and S. Johnson, "A fast Fourier transform compiler",
in Proc. of ACM SIGPLAN '99 Conf. Programming Language Design and
Implementation (PLDI), vol. 34 1999, pp. 169-180.
- M. Frigo and S. Johnson, "FFTW: An adaptive software architecture
for the FFT", in Proc. IEEE Intl. Conf. Acoustics, Speech and
Signal Processing, vol. 3, 1998, pp. 1381-1384.
Topics
- Bit-Reversal Permutation
- Iterative FFT
- Review of Modular Arithmetic
- Good-Thomas Algorithm
- Convolution Theorem
- Rader's Algorithm
- Bluestein's Algorithm
Lecture Slides
Programs
- fft.mws - Implementation of the FFT
Resources
Assignments
Created: July 5, 2005 by jjohnson@cs.drexel.edu