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	離散ウェーブレット変換	MODWT
分野	時系列解析	時系列解析
系統	Process / pipeline	Process / pipeline
提唱年	1992	1995
提唱者	Ingrid Daubechies	Donald B. Percival
種類	Hierarchical signal decomposition	Non-decimated multiresolution decomposition
原典	Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM.	Percival, D. B., & Walden, A. T. (1995). Wavelet Methods for Time Series Analysis. Cambridge University Press.
別名	DWT, Daubechies wavelets, Haar wavelet	MODWT, Stationary wavelet transform, Undecimated DWT
関連	1	2
概要	The discrete wavelet transform (DWT) is a fast, computationally efficient method for decomposing signals into different frequency and time components using orthogonal or biorthogonal wavelet functions. Developed rigorously by Ingrid Daubechies (1992) and built on Mallat's multiresolution decomposition theory (1989), the DWT employs filter banks to recursively split a signal into approximation (low-frequency) and detail (high-frequency) components. It has become the foundation for signal processing applications ranging from compression to feature extraction.	The maximal overlap discrete wavelet transform (MODWT) is a translation-invariant wavelet decomposition method that addresses a key limitation of the standard DWT: lack of shift invariance. Introduced by Percival and Walden (1995), MODWT applies the same wavelet filters at each scale without downsampling, producing an undecimated decomposition. Each detail and approximation coefficient array maintains the full length of the input signal, enabling both robust multi-scale analysis and translation-invariant feature extraction.