مقایسهٔ روش‌ها

	MODWT	تبدیل موجک گسسته	همبستگی موجک
حوزه	سری‌های زمانی	سری‌های زمانی	سری‌های زمانی
خانواده	Process / pipeline	Process / pipeline	Process / pipeline
سال پیدایش	1995	1992	1999
پدیدآور	Donald B. Percival	Ingrid Daubechies	Christopher Torrence
نوع	Non-decimated multiresolution decomposition	Hierarchical signal decomposition	Multi-scale correlation and phase
منبع بنیادین	Percival, D. B., & Walden, A. T. (1995). Wavelet Methods for Time Series Analysis. Cambridge University Press.	Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM.	Torrence, C., & Webster, P. J. (1999). Interdecadal changes in the ENSO–monsoon system. Journal of Climate, 12(8), 2679–2690.
نام‌های دیگر	MODWT, Stationary wavelet transform, Undecimated DWT	DWT, Daubechies wavelets, Haar wavelet	WTC, Wavelet coherency, Continuous wavelet coherence
مرتبط	2	1	1
خلاصه	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.	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.	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.