Tham khảo tài liệu 'lập trình c# all chap "numerical recipes in c" part 157', công nghệ thông tin phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Wavelet Transforms 591 The splitting point b must be chosen large enough that the remaining integral over b 1 is small. Successive terms in its asymptotic expansion are found by integrating by parts. The integral over a b can be done using dftint. You keep as many terms in the asymptotic expansion as you can easily compute. See 6 for some examples of this idea. More powerful methods which work well for long-tailed functions but which do not use the FFT are described in 7-9 . CITED REFERENCES AND FURTHER READING Stoer J. and Bulirsch R. 1980 Introduction to Numerical Analysis New York Springer-Verlag p. 88. 1 Narasimhan . and Karthikeyan M. 1984 IEEE Transactions on Antennas Propagation vol. 32 pp. 404-408. 2 Filon . 1928 Proceedings of the Royal Society of Edinburgh vol. 49 pp. 38-47. 3 Giunta G. and Murli A. 1987 ACM Transactions on Mathematical Software vol. 13 pp. 97107. 4 Lyness . 1987 in Numerical Integration P. Keast and G. Fairweather eds. Dordrecht Reidel . 5 Pantis G. 1975 Journal of Computational Physics vol. 17 pp. 229-233. 6 Blakemore M. Evans . and Hyslop J. 1976 Journal of Computational Physics vol. 22 pp. 352-376. 7 Lyness . and Kaper . 1987 SIAMJournal on Scientific and Statistical Computing vol. 8 pp. 1005-1011. 8 Thakkar . and Smith . 1975 Computer PhysicsCommunications vol. 10 pp. 73-79. 9 Wavelet Transforms Like the fast Fourier transform FFT the discrete wavelet transform DWT is a fast linear operation that operates on a data vector whose length is an integer power of two transforming it into a numerically different vector of the same length. Also like the FFT the wavelet transform is invertible and in fact orthogonal the inverse transform when viewed as a big matrix is simply the transpose of the transform. Both FFT and DWT therefore can be viewed as a rotation in function space from the input space or time domain where the basis functions are the unit vectors e or Dirac delta functions in the continuum .
