Порівняння методів

	Перетворення Фур'є та спектральний аналіз (FFT)	Варіаційний розклад мод (VMD)
Галузь	Обробка сигналів	Обробка сигналів
Родина	Machine learning	Machine learning
Рік появи	1965	2014
Автор методу	James Cooley & John Tukey (FFT)	Konstantin Dragomiretskiy & Dominique Zosso
Тип	Frequency-domain decomposition algorithm	Adaptive variational signal decomposition algorithm
Основоположне джерело	Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90), 297–301.	Dragomiretskiy, K., & Zosso, D. (2014). Variational mode decomposition. IEEE Transactions on Signal Processing, 62(3), 531–544.
Інші назви	Fast Fourier Transform, Discrete Fourier Transform, Spectral Analysis, Fourier Dönüşümü	VMD, Adaptive Signal Decomposition, Variational Signal Decomposition, Varyasyonel Mod Ayrıştırma
Пов'язані	2	2
Підсумок	The Fourier Transform decomposes a time-domain signal into its constituent sinusoidal frequencies, revealing the spectral content hidden within complex waveforms. Joseph Fourier introduced the continuous transform in 1822, but the computationally efficient Fast Fourier Transform (FFT) was formalized by James Cooley and John Tukey in 1965. Their landmark algorithm reduced the computational complexity from O(N²) to O(N log N), making large-scale spectral analysis practical across engineering, physics, and data science.	Variational Mode Decomposition (VMD) is a fully adaptive, non-recursive signal decomposition method introduced by Konstantin Dragomiretskiy and Dominique Zosso in 2014. It decomposes a real-valued input signal into a discrete number of sub-signals, called intrinsic mode functions (IMFs), each with a specific sparsity in the frequency domain. Unlike Empirical Mode Decomposition, VMD frames decomposition as a variational optimization problem solved via the Alternating Direction Method of Multipliers (ADMM), yielding robust and physically meaningful components.