Abstract
This paper considers the problem of signal decomposition and filtering by extending its scope to various signals that cannot be effectively dealt with existing methods. For the core of our methodology, we introduce a new approach, termed “ensemble patch transformation” that provides a framework for decomposition and filtering of signals; thus, as a result, it enhances identification of local characteristics embedded in a signal that is crucial for signal decomposition and designs flexible filters that allow various data analyses. In literature, there are some data-adaptive decomposition methods such as empirical mode decomposition (EMD) by Huang (Proc. R. Soc. London A 454:903–995, 1998). Along the same line of EMD, we propose a new decomposition algorithm that extracts essential components from a signal. Some theoretical properties of the proposed algorithm are investigated. To evaluate the proposed method, we analyze several synthetic examples and real signals.
Highlights
1 Introduction In this paper, we propose a new method for decomposition and filtering of signals, termed “ensemble patch transformation,” which adopts a multiscale concept of scale-space theory in computer vision of [1]
The second concept is “ensemble” that is obtained by shifting the time point t of the patch, which is suitable for representing the temporal variation of data efficiently by enhancement of the temporal resolution of them
We compare the proposed decomposition method with empirical mode decomposition (EMD), ensemble EMD (EEMD), and complete ensemble EMD with the adaptive noise (CEEMDAN) and various types of filters are designed for the analysis reflecting the characteristics of a given signal
Summary
We propose a new method for decomposition and filtering of signals, termed “ensemble patch transformation,” which adopts a multiscale concept of scale-space theory in computer vision of [1]. The proposed ensemble patch transformation consists of two key components. The first one is “patch process” that is defined as a data-dependent patch of data at a particular time point t. The patch process is designed for identifying local structures of data according to the sizes of patches. The second concept is “ensemble” that is obtained by shifting the time point t of the patch, which is suitable for representing the temporal variation of data efficiently by enhancement of the temporal resolution of them. Various statistics obtained from the proposed ensemble patches might be useful for data analysis
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