Ensemble patch transformation: a flexible framework for decomposition and filtering of signal

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.