Related papers: Signal Analysis based on Complex Wavelet Signs
We present a technique for measuring the transverse spatial properties of an optical wavefront. Intensity and phase profiles are recovered by analysis of a series of interference patterns produced by the combination of a scanning X-shaped…
A number of phenomena in various fields such as geology, atmospheric sciences, economics, to list a few, can be modeled as a fractional Brownian motion indexed by Hurst exponent $H$. This exponent is related to the degree of regularity and…
The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a…
Electromagnetic wave is reflected and refracted at interfaces, satisfying Fresnel-Snell law which is required by conservations of energy and momentum. If the incident angle is lower than the critical angle, we can use this Fresnel-Snell…
This paper establishes a comprehensive concentration theory for truncated signatures of Gaussian rough paths. The signature of a path, defined as the collection of all iterated integrals, provides a complete description of its geometric…
The objective of this work is to find temporal boundaries between signs in continuous sign language. Motivated by the paucity of annotation available for this task, we propose a simple yet effective algorithm to improve segmentation…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
In the analytic-Bargmann representation associated with the harmonic oscillator and spin coherent states, the wavefunction as entire complex functions can be factorized in terms of their zeros in a unique way. The Schr\"odinger equation of…
Three variants of the statistical complexity function, which is used as a criterion in the problem of detection of a useful signal in the signal-noise mixture, are considered. The probability distributions maximizing the considered variants…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine…
Symmetry is one of the significant visual properties inside an image plane, to identify the geometrically balanced structures through real-world objects. Existing symmetry detection methods rely on descriptors of the local image features…
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stability and invariance guarantees and therefore helps explain…
In this paper, estimation of mobility using received signal strength is presented. In contrast to standard methods, speed can be inferred without the use of any additional hardware like accelerometer, gyroscope or position estimator. The…
We introduce a new approach for Gaussianity testing using the envelope of a signal and its coefficient of variation. The envelope of a Gaussian signal follows the Rayleigh distribution, and given that the coefficient of variation of the…
A common signal is defined for any two signals which have non-zero correlation. A mathematical method is provided to extract the best obtainable common signal between the two signals. This analysis is extended to extracting common signal…
This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…
We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random…
We tackle the problem of recovering a complex signal $\boldsymbol x\in\mathbb{C}^n$ from quadratic measurements of the form $y_i=\boldsymbol x^*\boldsymbol A_i\boldsymbol x$, where $\boldsymbol A_i$ is a full-rank, complex random…
We present an optical wavefront shaping approach that allows tracking and localization of signal hidden inside or behind a scattering medium. The method combines traditional feedback based wavefront shaping together with a switch function,…