手法を比較

	MODWT	ウェーブレットコヒーレンス
分野	時系列解析	時系列解析
系統	Process / pipeline	Process / pipeline
提唱年	1995	1999
提唱者	Donald B. Percival	Christopher Torrence
種類	Non-decimated multiresolution decomposition	Multi-scale correlation and phase
原典	Percival, D. B., & Walden, A. T. (1995). Wavelet Methods for Time Series Analysis. Cambridge University Press.	Torrence, C., & Webster, P. J. (1999). Interdecadal changes in the ENSO–monsoon system. Journal of Climate, 12(8), 2679–2690.
別名	MODWT, Stationary wavelet transform, Undecimated DWT	WTC, Wavelet coherency, Continuous wavelet coherence
関連	2	1
概要	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.	Wavelet coherence (WTC) is a normalized measure of correlation between two time series in the time-frequency domain, eliminating the amplitude-dependence of the raw cross-wavelet transform. Introduced by Torrence and Webster (1999) and formalized by Grinsted, Moore, and Jevrejeva (2004), WTC quantifies how tightly two signals are coupled at each time-frequency point, independent of their individual power levels. It is the wavelet analog of classical spectral coherence, revealing time-localized relationships across all frequencies.