Linganisha mbinu

	Mabadiliko ya Fourier na Uchambuzi wa Spektra (FFT)	Uchanganuzi wa Njia Mbadala (Variational Mode Decomposition - VMD)
Nyanja	Uchakataji wa Mawimbi	Uchakataji wa Mawimbi
Familia	Machine learning	Machine learning
Mwaka wa asili	1965	2014
Mwanzilishi	James Cooley & John Tukey (FFT)	Konstantin Dragomiretskiy & Dominique Zosso
Aina	Frequency-domain decomposition algorithm	Adaptive variational signal decomposition algorithm
Chanzo asilia	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.
Majina mbadala	Fast Fourier Transform, Discrete Fourier Transform, Spectral Analysis, Fourier Dönüşümü	VMD, Adaptive Signal Decomposition, Variational Signal Decomposition, Varyasyonel Mod Ayrıştırma
Zinazohusiana	2	2
Muhtasari	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.