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Lập Trình C# all Chap "NUMERICAL RECIPES IN C" part 155

Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 155', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Chapter 13. Fourier and Spectral Applications 13.0 Introduction Fourier methods have revolutionized fields of science and engineering from radio astronomy to medical imaging from seismology to spectroscopy. In this chapter we present some of the basic applications of Fourier and spectral methods that have made these revolutions possible. Say the word Fourier to a numericist and the response as if by Pavlovian conditioning will likely be FFT. Indeed the wide application of Fourier methods must be credited principally to the existence of the fast Fourier transform. Better mousetraps stand aside If you speed up any nontrivial algorithm by a factor of a million or so the world will beat a path towards finding useful applications for it. The most direct applications of the FFT are to the convolution or deconvolution of data 13.1 correlation and autocorrelation 13.2 optimal filtering 13.3 power spectrum estimation 13.4 and the computation of Fourier integrals 13.9 . As important as they are however FFT methods are not the be-all and end-all of spectral analysis. Section 13.5 is a brief introduction to the field of time-domain digital filters. In the spectral domain one limitation of the FFT is that it always represents a function s Fourier transform as a polynomial in z exp 2 if A cf. equation 12.1.7 . Sometimes processes have spectra whose shapes are not well represented by this form. An alternative form which allows the spectrum to have poles in z is used in the techniques of linear prediction 13.6 and maximum entropy spectral estimation 13.7 . Another significant limitation of all FFT methods is that they require the input data to be sampled at evenly spaced intervals. For irregularly or incompletely sampled data other albeit slower methods are available as discussed in 13.8. So-called wavelet methods inhabit a representation of function space that is neither in the temporal nor in the spectral domain but rather something in-between. Section 13.10 is an introduction .