Related papers: Frames adapted to a phase-space cover
The capability of the adaptive optics to correct for the segmentation error is analyzed in terms of the residual wavefront RMS and the power spectral density of the phase. The analytical model and the end-to-end simulation give…
We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework is designed to allow for tile geometries which are…
Adaptive optics methods have long been used to perform complex light shaping at the output of a multimode fiber (MMF), with the specific aim of controlling the emitted beam in the near-field. Gaining control of other emission properties,…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
In this paper we propose a method for automatic local time adap- tation of the spectrogram of an audio signal, based on its decomposition within a Gabor multi-frame. The sparsity of the analyses within each individual frame is evaluated…
In this article, we present a general mode-conversion algorithm allowing to build an optical system composed of an alternation of phase masks and free propagations. The originality of our approach lies in the introduction of free parameters…
We introduce new frames, called \textit{metaplectic Gabor frames}, as natural generalizations of Gabor frames in the framework of metaplectic Wigner distributions. Namely, we develop the theory of metaplectic atoms in a full-general setting…
We present a method to synthesize phase screens for multi-wavelength, atmospheric wave optics simulations using fast Fourier transforms. We validate our work by comparing the theoretical, two-wavelength optical path length structure…
We discuss the design of ``wave packet systems'' that admit strong concentration properties in phase space. We make a connection between this problem and topics in signal processing related to the spectral behavior of spatial and…
The forthcoming communication systems are advancing towards improved flexibility in various aspects. Improved flexibility is crucial to cater diverse service requirements. This letter proposes a novel waveform design scheme that exploits…
We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working at an extremely high resolution (larger than 150x150). We use focal-plane images collected…
In a recent paper, we have shown that warped time-frequency representations provide a rich framework for the construction and study of smoothness spaces matched to very general phase space geometries obtained by diffeomorphic deformations…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
Microwave, submillimetre-wave, and far-infrared phased arrays are of considerable importance for astronomy. We consider the behaviour imaging phased arrays and interferometric phased arrays from a functional perspective. It is shown that…
Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…
General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
Nonstationary Gabor frames were recently introduced in adaptive signal analysis. They represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. In this paper…