Concept

Poisson summation formula

Related publications (34)

Succinct ordering and aggregation constraints in algebraic array theories

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring t ...

Elsevier Science Inc2024

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

Till Junge, Ali Falsafi, Martin Ladecký

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

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

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Recent trends of incorporating attention mechanisms in vision have led re- searchers to reconsider the supremacy of convolutional layers as a primary build- ing block. Beyond helping CNNs to handle long-range dependencies, Ramachandran et al. (2019) showed ...

2020

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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

In this thesis, we explore 3 main topics: non-uniform (in time) sub-sampling, QRS detection in an event-based sub-sampled ECG (electrocardiogram) and implementation on a low-power MCU (Micro Controller Unit). The main idea behind this work is to reduce the ...

2019

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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

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