Publications related to Poisson summation formula

Elimination of ringing artifacts by finite-element projection in FFT-based homogenization

Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond.rejc et al. (2014) [24] beyond the Fourier basis. In particular, we ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Frequency division using a soliton-injected semiconductor gain-switched frequency comb

Tobias Kippenberg, Junqiu Liu, Wenle Weng

With optical spectral marks equally spaced by a frequency in the microwave or the radio frequency domain, optical frequency combs have been used not only to synthesize optical frequencies from microwave references but also to generate ultralow-noise microw ...

2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

A Fourier-accelerated volume integral method for elastoplastic contact

Jean-François Molinari, Guillaume Anciaux, Lucas Henri Galilée Frérot

The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range of length-scale ...

2019

Spatially-Multiplexed Solitons in Optical Microresonators

Tobias Kippenberg, Maxim Karpov, Erwan Guillaume Albert Lucas, Arslan Sajid Raja

We simultaneously create stable solitons in up to three distinct mode families of a single crystalline MgF2 microresonator. The resulting Kerr combs are mutually coherent and have distinct repetition rates and are thus well suited for dual-comb application ...

IEEE2018

Ultralow-power chip-based soliton microcombs for photonic integration

Tobias Kippenberg, Michail Zervas, Bahareh Ghadiani, Junqiu Liu, Maxim Karpov, Hairun Guo, Martin Hubert Peter Pfeiffer, Arslan Sajid Raja, Nils Johan Engelsen, Botao Du

The generation of dissipative Kerr solitons in optical microresonators has provided a route to compact frequency combs of high repetition rate, which have already been employed for optical frequency synthesizers, ultrafast ranging, coherent telecommunicati ...

OPTICAL SOC AMER2018

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Michaël Unser, John Paul Ward, Quy Ha Nguyen

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...

2017

FRIDA: FRI-Based DOA Estimation For Arbitrary Array Layouts

Martin Vetterli, Eric Bezzam, Ivan Dokmanic, Robin Scheibler, Hanjie Pan

In this paper we present FRIDA—an algorithm for estimating directions of arrival of multiple wideband sound sources. FRIDA combines multi-band information coherently and achieves state- of-the-art resolution at extremely low signal-to-noise ratios. It work ...

IEEE2017

Partition function on spheres: How to use zeta function regularization

Alexander Monin

It is known that not all summation methods are linear and stable. Zeta function regularization is in general nonlinear. However, in some cases formal manipulations with zeta function regularization (assuming linearity of sums) lead to correct results. We c ...

American Physical Society2016

Generalized Poisson Summation Formula for Tempered Distributions

Michaël Unser, Quy Ha Nguyen

The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...

IEEE2015

Towards highest spectral efficiency: Optical sinc-shaped Nyquist pulses generation from rectangular frequency comb

Luc Thévenaz, Camille Sophie Brès, Marcelo Alfonso Soto Hernandez, Mohammad Amin Shoaie, Mohammad Mehdi Alem Karladani

In this paper, we review a method to produce optical sinc-shaped Nyquist pulses with unprecedented quality. The method is based on the synthesis of a rectangular shaped and phase-locked frequency comb from a combination of intensity modulators. The result ...

IEEE2014

Fourier Analysis of Functional Time Series, with Applications to DNA Dynamics

Shahin Tavakoli

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion ...

EPFL2014

Highly tunable method to generate sinc-shaped Nyquist pulses from a rectangular frequency comb

Luc Thévenaz, Camille Sophie Brès, Marcelo Alfonso Soto Hernandez, Mohammad Amin Shoaie, Mohammad Mehdi Alem Karladani

A method to produce highly-stable optical sinc-shaped pulses is proposed based on the generation of a rectangular-spectrum frequency comb. Nyquist pulses with

OSA2013

Optical sinc-shaped Nyquist pulses with very low roll-off generated from a rectangular frequency comb

Luc Thévenaz, Camille Sophie Brès, Marcelo Alfonso Soto Hernandez, Mohammad Amin Shoaie, Mohammad Mehdi Alem Karladani

High-quality optical sinc-shaped Nyquist pulses with a virtual zero roll-off factor are obtained from the generation of a phase-locked, rectangular-spectrum frequency comb. Tunability over more than 4 frequency decades is demonstrated with

Optical Society of America2013

Fourier Analysis Of Stationary Time Series In Function Space

Victor Panaretos, Shahin Tavakoli

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which gen ...

Institute of Mathematical Statistics2013

Shift-Invariant and Sampling Spaces Associated With the Fractional Fourier Transform Domain

Ayush Bhandari

Shift-invariant spaces play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. A special class of the shift-invariant spaces is the class of sampling spaces in which functions are determined ...

2012

Poisson Reduction by Distributions

Tudor Ratiu, Madeleine Jotz

It is shown that the singular Poisson reduction procedure can be improved for a large class of situations. In addition, Poisson reduction of orbit type manifolds is carried out in detail. ...

Springer Verlag2009

Rapid Fourier space solution of linear partial differential equations in toroidal magnetic confinement geometries

Laurent Villard, Trach-Minh Tran, Alberto Bottino, Sébastien Jolliet, Paolo Angelino, Ben McMillan

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We descr ...

Elsevier2009