Fast Fourier Transform and its C program
"Fast Fourier Transform and its C program" is published by China University of Science and Technology press. This book systematically introduces the theory and technology of Fourier transform, including the definition of Fourier transform (FT), its existence conditions and properties, the definition of discrete Fourier transform (DFT), its properties and spectrum aliasing and leakage caused by dispersion, fast Fourier transform (FFT) Based on the basic principle of the algorithm and the complex sequence base 2 algorithm and its utility, a fast algorithm and utility program for real sequence DFT, sine transform, cosine transform, Fourier series, spectral function approximation, power spectral estimation, convolution and correlation are given, and the 2D-DFT algorithm and two-dimensional real sequence 2d- DFT's Row-and-column algorithm and storage technology, 3D-DFT-like algorithm, 3D-DFT real-sequence dimensionality reduction algorithm and their utility programs. These are easily applied to the fast computation of higher dimensional DFT.1 Content Introduction
This book can be used as a graduate of science and Engineering, undergraduate senior students, especially in computational mathematics and application software, digital signal processing major students of textbooks or reference books, but also for the relevant engineering and technical personnel reference.2 directory
The 1th chapter is the Fourier series of the Fourier transformation 1.1-period function 1.1.13 Angle Series and its orthogonality 1.1.2 the Fourier series of the periodic function 1.1.3 Fourier progression 1.1.4 series expansion Fourier Complex form of Fourier series 1.1.6 optimal approximation of periodic function 1.2 Fourier integral 1.2.1 Fourier series and Fourier integral 1.2.2 Fourier integral convergence problem 1.2.3 Fourier integral complex form 1.3 The definition of Fourier transform 1.3.1 Fourier transformation 1.3.2 Fourier transform existence conditions 1.3.3 sine transform and cosine transform 1.3.4 Fourier transformation of common form 1.4 Fourier transform instance 1.4.1 Elementary function Fourier Transform instance 1.4.2 Generalized function Introduction 1.4.3δ function and its spectral function 1.5 fourier transformation symmetry 1.5.1 symmetric relation 1.5.2 The Fourier transformation of the double real function 1.6 Fourier transform properties 1.6.1 Basic Properties 1.6.2 convolution and correlation theorem 1.6.3 Parseval theorem exercise 2nd Chapter discrete Fourier transform 2.1 discrete time series Fourier transform 2.1.1 Discrete time series Fourier transform 2.1.2 Dtft Basic Properties 2.1.3 Convolution and correlation theorem 2.2 discrete Fourier transform definition 2.2.1 Fourier transform discretization 2.2.2 Discrete Fourier transform definition 2.2.3 The common form of discrete Fourier transformation 2.3 dft Nature 2.3.1 The basic nature of DFT 2.3.2 Discrete convolution and discrete correlation 2.3.3 Some special sequences of DFT2.3.4 real-sequence DFT technology 2.4 discrete sine transform and discrete cosine transform 2.4.1 discrete sine transform 2.4.2 discrete cosine transform 2.5 discrete Fourier series 2.5.1 discrete best square approximation 2.5.2 The discrete error 2.6.1 discrete sampling and spectral aliasing 2.6.2 finite window width and spectral leakage 2.6.3 continuous and discrete fourier transformation in discrete Fourier series 2.6 Fourier transform the 3rd chapter of DFT fast Calculation (FFT) Chapter 4th convolution and its fast algorithm 5th chapter Multidimensional Fourier transformation and its Fast algorithm Appendix Program index Reference
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