tailieunhanh - Algorithms for programmers ideas and source code

programmers who are interested in the treated algorithms and actually want to have/create working and reasonably optimized code. The printable full version will always stay online for free download. It is planned to also make parts of the TEXsources (plus the scripts used for automation) available. Right now a few files of the TEX sources and all extracted pseudo-code snippets1 are online. The C++-sources are online as part of FXT or hfloat (arithmetical algorithms). | Algorithms for programmers ideas and source code This document is work in progress read the important remarks near the beginning Jorg Arndt arndt@ This document1 was lATgX d at September 26 2002 Tills document is online at http fxt . It will stay available online for free. Contents Some important remarks about this document 6 List of important symbols 7 1 The Fourier transform 8 The discrete Fourier transform. 8 Symmetries of the Fourier transform. 9 Radix 2 FFT algorithms. 10 A little bit of notation. 10 Decimation in time DIT FFT. 10 Decimation in frequency DIF FFT. 13 Saving trigonometric computations. 15 Using lookup tables . 16 Recursive generation of the sin cos-values. 16 Using higher radix algorithms. 17 Higher radix DIT and DIF algorithms. 17 More notation . 17 Decimation in time. 17 Decimation in frequency. 18 Implementation of radix r px DIF DIT FFTs. 19 Split radix Fourier transforms SRFT . 22 Inverse FFT for free . 23 Real valued Fourier transforms . 24 Real valued FT via wrapper routines. 25 Real valued split radix Fourier transforms. 27 Multidimensional FTs . 31 Definition. 31 The row column algorithm . 31 The matrix Fourier algorithm MFA . 32 Automatic generation of FFT codes . 33 1 CONTENTS 2 2 Convolutions 36 Definition and computation via FFT. 36 Mass storage convolution using the MFA. 40 Weighted Fourier transforms . 42 Half cyclic convolution for half the price . 44 Convolution using the MFA. 44 The case R 2. 45 The case R 3. 45 Convolution of real valued data using the MFA. 46 Convolution without transposition using the MFA . 46 The z-transform ZT . 47 Definition of the ZT. 47 Computation of the ZT via convolution. 48 Arbitrary length FFT by ZT. 48 Fractional Fourier transform by ZT. 48 3 The Hartley transform HT 49 Definition .

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