Eugene Postnikov

Global and local spectral analysis of oscillating signals and images Eugene Postnikov

Document from the year 2014 in the subject Mathematics - Applied Mathematics, Kursk State University, language: Russian, abstract: This textbook presents the basics of the Fourier, the Gabor and the continuous wavelet analysis with the Morlet wavelet. The course started from the theoretical derivation based on the averaging approach, which is close connected with corresponding methods in the theory of dynamical systems. Thus, the introductory Chapter 1 is supplied with the examples illustrating analogies between the considered signal processing and the analytical approximations for ODE solutions. Chapter 2 explores the representation of the continuous wavelet transform with the Morlet wavelet as a solution of partial differential equations. Chapter 3 contains the practical recipes for MATLAB's code realizing the described algorithms and the examples of their implementations. ★★★★★★? ★★★★★★? ★★★★★★★★★★★★ ★★★★★★ ★★★★★★★★★★★★?? ?????, ★★★★★★ ? ★★★★★★★★★★★★ ??★★★★★-★★★★★★★★★★★★?? ? ★★★★★★??? ?????. ???? ★★★★★★???? ? ★★★★★★★★★★★★?? ★★★★★★, ★★★★★★????? ?? ★★★★★★? ★★★★★★????, ★★★★★★? ????? ★★★★★★ ? ★★★★★★★★★★★★???? ★★★★★★?? ? ★★★★★★ ★★★★★★★★★★★★ ★★★★★★. ????? ★★★★★★?, ★★★★★★? ????? 1 ★★★★★★★★★★★★?? ★★★★★★???, ★★★★★★★★★★★★??? ★★★★★★?? ★★★★★★??? ★★★★★★?? ? ★★★★★★★★★★★★? ★★★★★★★★★★★★? ??? ★★★★★★? ???. ????? 2 ★★★★★★??? ★★★★★★★★★★★★? ★★★★★★★★★★★★ ??★★★★★-★★★★★★★★★★★★?? ? ★★★★★★??? ????? ??? ★★★★★★? ★★★★★★★★★★★★???? ★★★★★★??? ? ★★★★★★? ★★★★★★?????. ????? 3 ★★★★★★?? ★★★★★★★★★★★★ ★★★★★★? ★★★★★★★★★★★★ ???? ??? MATLAB, ★★★★★★★★★★★★ ★★★★★★??? ★★★★★★???, ? ★★★★★★? ?? ★★★★★★????.