algorithm machine calculation complex fourier von cooley james (2 Ergebnisse)

TUKEY, John W. An Algorithm for the Machine Calculation of Complex Fourier Series. [within] Mathematics of Computation, volume 19, no.90 pp.297-301. Providence: National Academy of Sciences, 1965. First edition of Cooley & Tukey's article entitled An Algorithm for the Machine Calculation of Complex Fourier Series within the periodical Mathematics of Computation, volume 19, no.90 pp.297-301. This article is the introduction of the Cooley-Tukey algorithm (known as the Fast Fourier Transform, FFT). Original blue printed wrappers. Printed in black. Some very light wear along spine, otherwise wrappers and text are all about fine. 'Cooley and Tukey's paper introduced the fast Fourier transform algorithm (FFT) to the scientific computing world. The great economies of calculation effected by FFT made possible a number of major advances in scientific computing, including digital filtering, spectral analysis, and digital methods for processing speech, music, and images' (Origins of Cyberspace, 548). 'The introduction in 1965 of the Cooley-Tukey algorithm (known as the Fast Fourier Transform, FFT) greatly increases the speed of calculations and thereby the usefulness of the Fourier methods', Gedeon p.178. "With John Tukey, Cooley wrote the fast Fourier transform (FFT) paper (Cooley and Tukey 1965) that has been credited with introducing the algorithm to the digital signal processing and scientific community in general." Tukey is also known as the possible creator of the word "bit" in computer terminology. (Computer Pioneers by J. A. N. Lee) According to Christies "The paper had its basis in Tukey's demonstration that "if NI, the number of terms in a Fourier series, is a composite, N = ab, then the series can be expressed as an -term series of subseries of terms each. If one were computing all values of the series, this would reduce the number of operations from 2 to N log N. . Tukey's form of the algorithm, with repeated factors, has the great advantage that a computer program need only contain instructions for the algorithm for the common factor. Indexed loops repeat this basic calculation and permit one to iterate up to an arbitrary high NI, limited only by time and storage" (Cooley 1987, 133, 136)". HBS 68508. $1,350.

Contained in Mathematics of Computation, Vol. 19, No. 90, pp. 297-301. 8vo. pp. 177-364. Original printed wrappers bound in. Black cloth, printed paper spine label. Institutional exlib stamp on printed wrapper cover, ownership marks on printed covers. Fine. FIRST EDITION. This important work on the fast Fourier transform (FFT) algorithm, which is an efficient algorithm to compute the discrete Fourier transform (DFT) and its inverse. FFTs are of great importance to a wide variety of applications, from digital signal processing and solving partial differential equations to algorithms for quick multiplication of large integers. "By far the most common FFT is the Cooley-Tukey algorithm. This is a divide and conquer algorithm that recursively breaks down a DFT of any composite size N = N1N2 into many smaller DFTs of sizes N1 and N2, along with O(N) multiplications by complex roots of unity, traditionally called twiddle factors (after Gentleman and Sande, 1966). This method (and the general idea of an FFT) was popularized by a publication of J. W. Cooley and J. W. Tukey in 1965, but it was later discovered that those two authors had independently re-invented an algorithm known to Carl Friedrich Gauss around 1805 (and subsequently rediscovered several times in limited forms). The most well-known use of the Cooley-Tukey algorithm is to divide the transform into two pieces of size N / 2 at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general (as was known to both Gauss and Cooley/Tukey). These are called the radix-2 and mixed-radix cases, respectively (and other variants such as the split-radix FFT have their own names as well). Although the basic idea is recursive, most traditional implementations rearrange the algorithm to avoid explicit recursion. Also, because the Cooley-Tukey algorithm breaks the DFT into smaller DFTs, it can be combined arbitrarily with any other algorithm for the DFT." [Wikip.]. Norman, Origins of Cyberspace 548.