Related papers: Topological phase estimation method for reparamete…
The well-known stationary phase formula gives us a way to precisely compute oscillating integrals so long as the symbol is regular enough (in comparison to the large parameter controlling the oscillation). However in a number of…
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…
We analyze the convergence of piecewise collocation methods for computing periodic solutions of general retarded functional differential equations under the abstract framework recently developed in [S. Maset, Numer. Math. (2016)…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…
Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify…
In current paper, distortions in digital demodulation schemes with harmonic phase modulation for interferometric optical sensors are considered. In particular, the influence of target signal variations on phase demodulation errors is…
Phase estimation protocols provide a fundamental benchmark for the field of quantum metrology. The latter represents one of the most relevant applications of quantum theory, potentially enabling the capability of measuring unknown physical…
Topological data analysis provides a set of tools to uncover low-dimensional structure in noisy point clouds. Prominent amongst the tools is persistence homology, which summarizes birth-death times of homological features using data objects…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
In this paper we present a multiresolution-based method for period determination that is able to deal with unevenly sampled data. This method allows us to detect superimposed periodic signals with lower signal-to-noise ratios than in…
Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a…
We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…
Assessment of voice signals has long been performed with the assumption of periodicity as this facilitates analysis. Near periodicity of normal voice signals makes short-time harmonic modeling an appealing choice to extract vocal feature…
In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…