Lecture 2: The Fast Fourier Transform

Background Material

• Recurrence Relations
• Growth Rates and Asymptotic Analysis
• Matrix Notation and Manipulation

Reading

• Chapter 9 of Lipson
• 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

• The Cooley-Tukey fast Fourier transform (FFT)
• Rader's Algorithm

Lecture Slides

• The FFT fft.ppt
• The 3 primes algorithm fast.ppt

Maple worksheets and programs

• fft.mws - Implementation of the FFT
• threeprimes.mws - Implementation of the 3 primes algorithm

Resources

• www.fftw.org (FFTW Web site)

Assignments

• Assignment 1