Discrete frequency slice wavelet transform. (November 2017)

• Record Type: Journal Article
• Authors: Yan, Zhonghong; Tao, Ting; Jiang, Zhongwei; Wang, Haibin
• Is Part Of: Mechanical systems and signal processing. Volume 96(2017)
• Page Start: 385
• Page End: 392
• Publication Date: 2017-11
• Subjects: Time-frequency analysis -- Free style wavelet base -- New method of signal processing -- Bio-signal decomposition and reconstruction -- Signal filter; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2017.04.019
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: FSWT showed the efficient TFR in an easy way without strict limitation. Discrete FSWT (DFSWT) as well as FSWT are defined directly in frequency domain. DFSWT keeps its properties in time-frequency domain as FSWT. The properties are FSWT decomposition, reconstruction and filter design etc. The original signal is decomposed and reconstructed on a Chosen Frequency Domains. The decomposition and reconstruction are not completed on all frequency components. Some conclusions are drawn that the concept of CFD is very useful to application. DFSWT can become a simple and easy tool of TFR method. DFSWT also provides a new idea of low speed sampling of high frequency signal. Abstract: This paper introduces a new kind of Time-Frequency Representation (TFR) method called Discrete Frequency Slice Wavelet Transform (DFSWT). It is an improved version of Frequency Slice Wavelet Transform (FSWT). The previous researches on FSWT show that it is a new efficient TFR in an easy way without strict limitation as traditional wavelet theory. DFSWT as well as FSWT are defined directly in frequency domain, and still keep its properties in time-frequency domain as FSWT decomposition, reconstruction and filter design, etc. However, the original signal is decomposed and reconstructed on a Chosen Frequency Domains (CFD) as need of application. CFD means that the decomposition and reconstruction are not completed on all frequency components. At first, it is important to discuss the necessary condition of CFD to reconstruct the original signal. And then based on norm l2, an optimization algorithm is introduced to reconstruct the original signal even accurately. Finally, for a test example, the TFR analysis of a real life signal is shown. Some conclusions are drawn that the concept of CFD is very useful to application, and the DFSWT can become a simple and easy tool of TFR method, and also provide a new idea of low speed sampling of high frequency signal in applications.