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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 obtain new Fourier interpolation and uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa [11] and the second author [12]. We show that the only Schwartz function which, together with its Fourier transform ...
Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...
Sampling has always been at the heart of signal processing providing a bridge between the analogue world and discrete representations of it, as our ability to process data in continuous space is quite limited. Furthermore, sampling plays a key part in unde ...
We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data ...
In every dimension d >= 2, we give an explicit formula that expresses the values of any Schwartz function on R-d only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres whose radius is the square roo ...
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice---a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng, Kritzer, Hickernell (C ...
Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and proso ...
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 ...
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 ...