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This dissertation presents two signal processing methods using specially designed localized kernels for parameter recovery under noisy condition. The first method addresses the estimation of frequencies and amplitudes in multidimensional…
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…
Complex frequency excitations, oscillating signals whose amplitude decreases exponentially in time, have recently been demonstrated to significantly increase the effective quality factor of mechanical resonators. In this work, we…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
In this paper we provide a complete link between dissipation theory and a celebrated result on stability analysis with integral quadratic constraints. This is achieved with a new stability characterization for feedback interconnections…
Signals comprised of a stream of short pulses appear in many applications including bio-imaging and radar. The recent finite rate of innovation framework, has paved the way to low rate sampling of such pulses by noticing that only a small…
Scanning Probe Microscopy (SPM) is the primary tool for exploring nanoscale functionality, yet standard single-frequency operation is fundamentally limited, because the dynamic tip-sample interaction is mathematically underdetermined. While…
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,…
Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
Many control and detection applications require real-time analysis of signals from sensors, in order to quickly and accurately act upon events revealed by the sensors. Such signal analysis benefits from statistical models of signal and…
Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital conversion technique, where the measurements are recorded only when there is a significant change in the signal amplitude. Neuromorphic sampling has paved the way…
The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
Parameter estimation on gravitational wave signals from compact binary coalescence (CBC) requires the evaluation of computationally intensive waveform models, typically the bottleneck in the analysis. This cost will increase further as low…
Dynamic factor models are often estimated by point-estimation methods, disregarding parameter uncertainty. We propose a method accounting for parameter uncertainty by means of posterior approximation, using variational inference. Our…
Sensing periodic-fields using quantum sensors has been an active field of research. In many of these scenarios, the quantum state of the probe is flipped regularly by the application of $\pi$-pulses to accumulate information about the…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
We propose and analyze a versatile and efficient multiparameter quantum sensing protocol, which simultaneously estimates many non-commuting and time-dependent signals that are coherently or incoherently coupled to sensing particles. Even in…