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In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discr ...
Fourier transforms are an often necessary component in many computational tasks, and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choi ...
We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...
This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
This chapter presents an overview of techniques used for the analysis, edition, and synthesis of time series, with a particular emphasis on motion data. The use of mixture models allows the decomposition of time signals as a superposition of basis function ...
This paper introduces a recent innovation in dealing with non-periodic behavior often referred to as transients in perturbative experiments. These transients can be the result from the unforced response due to the initial condition and other slow trends in ...
The analysis of the effect of sub-sampling phase detector (SSPD) timing nonidealities on Type-I sub-sampling phase-locked loop (SSPLL) is presented. The nonidealities considered are the delay between the complementary sampling clocks and the propagation de ...
We propose a methodology combining physical modelling and machine learning (ML) to estimate the apparent ground thermal diffusivity at the scale of a country. Based on ground temperature time series at different depths, we estimate the diffusivity at 49 Sw ...
This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...
The discrete time analysis of the phase detector linear range extension in the first and the second order sub sampling phase-locked loop (SSPLL) is presented. The aim is to understand how much the stability and the pull-in range are affected by the linear ...