# 14.4: Appendix 4 - Programs for Short FFTs


This appendix will discuss efficient short FFT programs that can be used in both the The Cooley-Tukey Fast Fourier Transform Algorithm and the The Prime Factor and Winograd Fourier Transform Algorithms. Links and references are given to Fortran listings that can be used "as is" or put into the indexed loops of existing programs to give greater efficiency and/or a greater variety of allowed lengths. Special programs have been written for lengths: $$N=2,3,4,5,7,8,9,11,13,16,17,19,25,...$$

In the early days of the FFT, multiplication was done in software and was, therefore, much slower than an addition. With modem hardware, a floating point multiplication can be done in one clock cycle of the computer, microprocessor, or DSP chip, requiring the same time as an addition. Indeed, in some computers and many DSP chips, both a multiplication and an addition (or accumulation) can be done in one cycle while the indexing and memory access is done in parallel. Most of the algorithms described here are not hardware architecture specific but are designed to minimize both multiplications and additions.

The most basic and often used length FFT (or DFT) is for N=2N=2" role="presentation" style="position:relative;" tabindex="0">

This page titled 14.4: Appendix 4 - Programs for Short FFTs is shared under a CC BY license and was authored, remixed, and/or curated by C. Sidney Burrus.