http://www.norbertwiener.umd.edu/Research/Duhamel_Vetterli_FFT_90.pdf

Fast fourier transforms: a tutorial review and a state of the art

Note: V. K. Madisetti, D. B. Williams, Eds. Reference LCAV-CHAPTER-2005-009 Record created on 2005-06-27, modified on 2017-05-12

Fast Fourier transforms: a tutorial review and a state of the art

A global network of ground-based Fourier transform spectrometers has been founded to remotely measure column abundances of CO_2, CO, CH_4, N_(2)O and other molecules that absorb in the near-infrared. These measurements are directly comparable with the near-infrared total column measurements from space-based instruments. With stringent requirements on the instrumentation, acquisition procedures, data processing and calibration, the Total Carbon Column Observing Network (TCCON) achieves an
accuracy and precision in total column measurements that is unprecedented for remotesensing observations (better than 0.25% for CO_2). This has enabled carbon-cycle science
investigations using the TCCON dataset, and allows the TCCON to provide a link between satellite measurements and the extensive ground-based in situ network.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2010.0240

The Total Carbon Column Observing Network

For some time the Fourier transform has served as a bridge between the time domain and the frequency domain. It is now possible to go back and forth between waveform and spectrum with enough speed and economy to create a whole new range of applications for this classic mathematical device. This article is intended as a primer on the fast Fourier transform, which has revolutionized the digital processing of waveforms. The reader's attention is especially directed to the IEEE Transactions on Audio and Electroacoustics for June 1969, a special issue devoted to the fast Fourier transform.

A guided tour of the fast Fourier transform

This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued split-radix FFT, an algorithm that uses fewer operations than any other real-valued power-of-2-length FFT. We also compare the performance of inherently real-valued transform algorithms such as the fast Hartley transform (FHT) and the fast cosine transform (FCT) to real-valued FFT algorithms for the computation of power spectra and cyclic convolutions. Comparisons of these techniques reveal that the alternative techniques always require more additions than a method based on a real-valued FFT algorithm and result in computer code of equal or greater length and complexity.

Real-valued fast Fourier transform algorithms

Fast Fourier analysis (FFA) and fast Fourier synthesis (FFS) algorithms are developed for computing the discrete Fourier transform of a real series, and for synthesizing a real series from its complex Fourier coefficients. A FORTRAN program implementing both algorithms is given in the Appendix.

A radix-eight fast Fourier transform subroutine for real-valued series

This discussion served as an introduction to the Hardware Implementations Session of the IEEE Workshop on Fast Fourier Transform Processing. It introduces the problems associated with implementing the FFT algorithm in hardware and provides a frame of reference for characterizing specific implementations. Many of the design options applicable to an FFT processor are described, and a brief comparison of several machine organizations is given.

Fast Fourier transform hardware implementations--An overview

A list of features that serves to characterize an FFT processor was developed during a working session of the IEEE Workshop on Fast Fourier Transform Processing. Based on this list, information was requested on all of the processors that were known to the Workshop Organizing Committee. A copy of the table shown in this paper was sent to 20 companies with the request that each company specify the data relating to their machine in the form they would like it to be printed. The table represents a compilation of the returns.

https://ieeexplore.ieee.org/iel6/8337/26068/01162048.pdf

Fast Fourier transform hardware implementations--A survey

A fast Fourier transform (FFT) algorithm is presented for an unstructured, parallel ensemble of computing elements with global control. The procedure makes efficient use of a fixed-size memory and minimizes data transmission between computing elements. Included are some practical considerations of the trade-offs between element utilization and gain of computing speed via parallelism.

G. Bergland

Papers

A radix-eight fast Fourier transform subroutine for real-valued series

Fast Fourier transform hardware implementations--An overview

Fast Fourier transform hardware implementations--A survey

A fast Fourier transform global, highly parallel processor