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| Dyskretna transformata falkowa× | MODWT× | |
|---|---|---|
| Dziedzina | Szeregi czasowe | Szeregi czasowe |
| Rodzina | Process / pipeline | Process / pipeline |
| Rok powstania≠ | 1992 | 1995 |
| Twórca≠ | Ingrid Daubechies | Donald B. Percival |
| Typ≠ | Hierarchical signal decomposition | Non-decimated multiresolution decomposition |
| Źródło pierwotne≠ | Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM. DOI ↗ | Percival, D. B., & Walden, A. T. (1995). Wavelet Methods for Time Series Analysis. Cambridge University Press. link ↗ |
| Inne nazwy | DWT, Daubechies wavelets, Haar wavelet | MODWT, Stationary wavelet transform, Undecimated DWT |
| Pokrewne≠ | 1 | 2 |
| Podsumowanie≠ | 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. |
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