Phase reconstruction from oscillatory data with iterated Hilbert transform embeddings—Benefits and limitations

Truncated Hilbert transform and image reconstruction from limited tomographic data

A data sufficiency condition for 2D or 3D region-of-interest (ROI) reconstruction from a limited family of line integrals has recently been introduced using the relation between the backprojection of a derivative of the data and the Hilbert transform of the image along certain segments of lines covering the ROI. This paper generalizes this sufficiency condition by showing that unique and stable...

Asymptotically exact AM-FM decomposition based on iterated hilbert transform

This paper presents a multicomponent sinusoidal model of speech signals, obtained through a rigorous mathematical formulation that ensures an asymptotically exact reconstruction of these nonstationary signals, despite the presence of transients, voiced segments, or unvoiced segments. This result has been obtained by means of the iterated use of the Hilbert transform, and the convergence propert...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data

Accurate Instantaneous Frequency Estimation with Iterated Hilbert Transform and Its Application

Iterated Hilbert transform (IHT) is a new method for multicomponent demodulation. The principle of IHT is introduced, and some of its properties are researched. Although the amplitudes of the demodulated components obtained by IHT are accurate, there are limitations in the direct estimation of instantaneous frequencies via the extracted phases, so a smoothed instantaneous frequency estimation (...