arXiv subjects

Alessandro Mazzoccoli

Publications and source records attributed to Alessandro Mazzoccoli.

4 recordsLinked to original sources

arXiv2026

Chirp-Induced Non-Separable Gabor Windows on $\mathbb{R}^d$

We construct an explicit class of non-separable Gabor windows on $L^2(\R^d)$ by applying chirp deformations to tensor-product dual pairs on separable lattices. Starting from one-dimensional dual Gabor frames, we first obtain separable higher-dimensional dual pairs by tensorization. We then transport these systems through the unitary chirp operator $U_C f(x)=e^{\pi i x^T Cx}f(x)$ and the associated phase-space shear, obtaining Gabor systems on lower block-triangular lattices of the form $ \Lambda_{A,B,C}=\{(Ak,CAk+B\ell):k,\ell\in\Z^d\}. $ {The construction is governed by a single unitary conjugacy identity for the mixed Gabor reconstruction operator. As consequences, compact support, smoothness, frame bounds, exact duality, canonical duals, and approximate-duality errors are transported without loss.} {We also record a covariance-level diagnostic, depending on a chosen STFT reference window, which describes the second-order time--frequency tilt induced by the chirp. This diagnostic is separated from the unchanged frame stability constants and is not used here to claim improved sparsity, denoising, conditioning, or computational complexity.}

math.FA↗

arXiv2025

Symmetry, Scaling, and Optimal Time-Frequency Concentration: Minimising the Heisenberg Uncertainty in Piecewise-Polynomial and Wavelet Dictionaries

In this work, we introduce a hierarchy of function classes defined on a fixed compact interval, along with tailored uncertainty operators. We establish key properties of the associated uncertainty product, showing that it is invariant under scale and translation transformations. Notably, we prove that the infimum of the uncertainty within the asymmetric class is attained in the even subclass. Within two specific wavelet dictionaries, we identify the tent function as the unique minimiser of the time-frequency uncertainty, achieving a value of $U = \frac{3}{10}$. Additionally, we analyse the family of $p$-fold self-convolutions of the rectangle function, $\operatorname{rect}^{\{p\}}$, demonstrating that the uncertainty decreases monotonically towards the Heisenberg bound $ \frac{1}{4} $ as $p \to \infty$. These findings unify and explain various empirical observations from the literature on adaptive wavelet design and Gabor frame stability, and suggest a principled approach to constructing dictionaries with provably optimal joint localisation properties.

math.FA↗

arXiv2022

Wavelet analysis and energy-based measures for oil-food price relationship as a footprint of financialisation effect

In this paper we exploit the wavelet analysis approach to investigate oil-food price correlation and its determinants in the domains of time and frequency. Wavelet analysis is able to differentiate high frequency from low frequency movements which correspond, respectively, to short and long run dynamics. We show that the significant local correlation between food and oil is only apparent and this is mainly due both to the activity of commodity index investments and, to a lesser extent, to a growing demand from emerging economies. Moreover, the activity of commodity index investments gives evidence of the overall financialisation process. In addition, we employ wavelet entropy to assess the predictability of the time series under consideration at different frequencies. We find that some variables share a similar predictability structure with food and oil. These variables are the ones that move the most along with oil and food. We also introduce a novel measure, the Cross Wavelet Energy Entropy Measure (CWEEM), based on wavelet transformation and information entropy, with the aim of quantifying the intrinsic predictability of food and oil given demand from emerging economies, commodity index investments, financial stress, and global economic activity. The results show that these dynamics are best predicted by global economic activity at all frequencies and by demand from emerging economies and commodity index investments at high frequencies only.

q-fin.CP↗

arXiv2018

Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension

We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term, in the case of large dissipation. We assume the system to be conservative in the absence dissipation, so that the forcing term is --- up to the sign --- the gradient of a potential energy, and both the mass and damping matrices to be symmetric and positive definite. Further, we assume a non-degeneracy condition on the forcing term, essentially that the time-average of the potential energy has a strict local minimum. On the contrary, no condition is assumed on the forcing frequency; in particular we do not require any Diophantine condition. We prove that, under the assumptions above, a response solution always exist provided the dissipation is strong enough. This extends results previously available in literature in the one-dimensional case.

math.DS↗