Empirical Wavelet Transform (EWT)

A fully data-driven precursor to EWT that decomposes a signal into Intrinsic Mode Functions (IMFs) without a predefined basis. Unlike EWT, which segments the Fourier spectrum, EMD uses an iterative sifting process based on local extrema to extract oscillatory modes. This makes EMD highly adaptive but mathematically less tractable and prone to mode mixing, where disparate frequencies appear in a single IMF. EWT addresses this by providing a rigorous wavelet framework for the extracted modes.

The classical method for time-frequency analysis that computes the Fourier transform over windowed signal segments. The STFT uses a fixed window length, resulting in a uniform time-frequency resolution across the entire plane—a rigid trade-off governed by the Heisenberg-Gabor uncertainty principle. EWT improves upon this by adaptively constructing wavelet filters based on the signal's own spectral content, allowing for multi-resolution analysis that captures both transient and steady-state features with optimal localization.

A transform that provides a highly redundant time-scale representation by correlating a signal with scaled and translated versions of a mother wavelet. The CWT offers excellent multi-resolution properties, but its continuous nature makes it computationally intensive and non-adaptive—the mother wavelet must be chosen a priori. EWT bridges the gap by building a custom wavelet basis directly from the signal's Fourier spectrum, combining the adaptivity of EMD with the mathematical rigor of wavelet theory.

A post-processing reassignment technique that sharpens time-frequency representations by concentrating diffuse energy along instantaneous frequency ridges. SST is often applied to the CWT or STFT to improve component readability. EWT operates on a similar principle of identifying spectral supports but uses this information to construct adaptive bandpass filters for direct mode extraction, rather than reassigning existing coefficients. Both methods aim to provide highly localized, readable time-frequency decompositions.

A non-recursive method that extracts a predefined number of band-limited Intrinsic Mode Functions concurrently by solving a variational optimization problem. VMD minimizes the bandwidth of each mode in the spectral domain, making it robust to noise and sampling errors. EWT shares VMD's goal of extracting compact spectral modes but does so through a segmentation-and-filtering approach rather than variational optimization, often resulting in lower computational complexity for signals with well-separated spectral supports.

A two-step adaptive analysis framework combining EMD for decomposition and the Hilbert spectral analysis for calculating instantaneous frequencies. The HHT is designed for non-stationary and nonlinear signals. EWT can serve as a direct replacement for the EMD step, providing a more mathematically grounded decomposition into amplitude-modulated and frequency-modulated (AM-FM) components. The resulting modes can then be analyzed with the Hilbert transform to extract physically meaningful instantaneous attributes.