مقایسهٔ روش‌ها

	حذف نویز سیگنال با تبدیل موجک (آستانه‌گذاری نرم)	تبدیل فوریه و تحلیل طیفی (FFT)	تجزیه مُد نوسانی (VMD)
حوزه	پردازش سیگنال	پردازش سیگنال	پردازش سیگنال
خانواده	Machine learning	Machine learning	Machine learning
سال پیدایش	1995	1965	2014
پدیدآور	David Donoho	James Cooley & John Tukey (FFT)	Konstantin Dragomiretskiy & Dominique Zosso
نوع	Non-parametric signal estimation	Frequency-domain decomposition algorithm	Adaptive variational signal decomposition algorithm
منبع بنیادین	Donoho, D. L. (1995). De-noising by soft-thresholding. IEEE Transactions on Information Theory, 41(3), 613–627.	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.
نام‌های دیگر	Wavelet Shrinkage, Donoho-Johnstone Denoising, Soft Thresholding Denoising, Sinyal Gürültü Giderme	Fast Fourier Transform, Discrete Fourier Transform, Spectral Analysis, Fourier Dönüşümü	VMD, Adaptive Signal Decomposition, Variational Signal Decomposition, Varyasyonel Mod Ayrıştırma
مرتبط	3	2	2
خلاصه	Wavelet signal denoising, introduced by David Donoho in 1995, is a non-parametric technique that removes noise from one-dimensional or multidimensional signals by decomposing them into wavelet coefficients, suppressing small coefficients that likely represent noise via a soft-thresholding operator, and reconstructing a smooth estimate. It is widely used in biomedical signal processing, geophysics, audio engineering, and image analysis where the underlying signal is assumed to be sparse or piecewise smooth.	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.