مقایسهٔ روش‌ها

	تجزیه مُد نوسانی (VMD)	تبدیل فوریه و تحلیل طیفی (FFT)
حوزه	پردازش سیگنال	پردازش سیگنال
خانواده	Machine learning	Machine learning
سال پیدایش	2014	1965
پدیدآور	Konstantin Dragomiretskiy & Dominique Zosso	James Cooley & John Tukey (FFT)
نوع	Adaptive variational signal decomposition algorithm	Frequency-domain decomposition algorithm
منبع بنیادین	Dragomiretskiy, K., & Zosso, D. (2014). Variational mode decomposition. IEEE Transactions on Signal Processing, 62(3), 531–544.	Cooley, J. W., & Tukey, J. W. (1965). An algorithm for the machine calculation of complex Fourier series. Mathematics of Computation, 19(90), 297–301.
نام‌های دیگر	VMD, Adaptive Signal Decomposition, Variational Signal Decomposition, Varyasyonel Mod Ayrıştırma	Fast Fourier Transform, Discrete Fourier Transform, Spectral Analysis, Fourier Dönüşümü
مرتبط	2	2
خلاصه	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.	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.