Real Wavelet Transform-Based Phase Information Extraction Method: Theory and Demonstrations

Complex wavelet transform (CoWT)-based phase information (PI) extraction methods are popular. None of them is simultaneously simple, fast, and nonredundant. Real discrete wavelet transform (RDWT) is simple, fast, and nonredundant, but it is usually regarded to be lacking PI. After finding out that RDWT conserves the PI of an analyzed signal, this paper proposed three RDWT-based PI extraction methods and proved that RDWT-based PI extraction methods are equal to CoWT-based ones from the mathematical point of view. Therefore, RDWT-based methods not only can extract PI but also can inherit all merits of RDWT. This paper further presented a quadrature procedure to extract the actual phase of single-frequency or asymptotic signals. Test examples demonstrated that the extracted PI by using the CoWT- and RDWT-based methods is almost the same, and the extracted phase curves by using the RDWT-based quadrature method are really the actual ones. Some engineering applications of the proposed method are discussed, and the PI extraction programs of the method are given.