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This book explores both the practical and theoretical aspects of the Discrete Fourier Transform, one of the most widely used tools in science, engineering, and computational mathematics. Designed to be accessible to an audience with diverse interests and mathematical backgrounds, the book is written in an informal style and is supported by many examples, figures, and problems. Conceived as an qowner'sq manual, this comprehensive book covers such topics as the history of the DFT, derivations and properties of the DFT, comprehensive error analysis, issues concerning the implementation of the DFT in one and several dimensions, symmetric DFTs, a sample of DFT applications, and an overview of the FFT.An Ownersa#39; Manual for the Discrete Fourier Transform William L. Briggs, Van Emden Henson. The first step ... The integral 1 g(wi : h/l g(p, Acj)e-i21rwpdp must be approximated for j = 0, 1, ..., M a€” 1. The trapezoid ... We are at liberty to reconstruct at any convenient sampling of (:c, y) within the region {(1, y)|1a#39;2 + g2 alt; 1}. It seemsanbsp;...

Title:The DFT
Author:William L. Briggs, Van Emden Henson
Publisher:SIAM - 1995


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