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Inside Collection (Book): Fast Fourier Transforms

This appendix will discuss efficient short FFT programs that can be used in both the Cooley-Tukey and the Prime Factor FFT 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:

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

Code for other short lengths such as the primes

If these short FFTs are used as modules in the basic prime factor algorithm (PFA), then the straight forward development used for the modules in Figure 17.12 are used. However if the more complicated indexing use to achieve in-order, in-place calculation used in {xxxxx} require different code.

For each of the indicated lengths, the computer code is given in a Connexions module.

They are not in the collection Fast Fourier Transforms as the printed version would be too long. However, one can link to them on-line from the following buttons:

Versions for the in-place, in-order prime factor algorithm {pfa} can be obtained from: A technical report that describes the length 11, 13, 17, and 19 is in {report 8105} and another technical report that describes a program that will automatically generate a prime length FFT and its flow graph si in {report xxx}.- « Previous module in collection Appendix 3: FFT Computer Programs
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Comments:"The Fast Fourier Transform (FFT) is a landmark algorithm used in fields ranging from signal processing to high-performance computing. First popularized by two American scientists in 1965, the […]"