Related papers: Sampling and Frequency Warping
In this paper we study the general reconstruction of a compactly supported function from its Fourier coefficients using compactly supported shearlet systems. We assume that only finitely many Fourier samples of the function are accessible…
Reconstructing a band-limited function from its finite sample data is a fundamental task in signal analysis. A Gaussian regularized Shannon sampling series has been proved to be able to achieve exponential convergence for uniform sampling.…
Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction…
Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware…
Choosing an appropriate frequency definition and norm is critical in graph signal sampling and reconstruction. Most previous works define frequencies based on the spectral properties of the graph and use the same frequency definition and…
Recently efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized…
In order to produce high dynamic range images in radio interferometry, bright extended sources need to be removed with minimal error. However, this is not a trivial task because the Fourier plane is sampled only at a finite number of…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
In a series of recent papers (Adcock, Hansen and Poon, 2013, Appl. Comput. Harm. Anal. 45(5):3132-3167), (Adcock, Gataric and Hansen, 2014, SIAM J. Imaging Sci. 7(3):1690-1723) and (Adcock, Hansen, Kutyniok and Ma, 2015, SIAM J. Math. Anal.…
In this paper, we investigate frames for $L_2[-\pi,\pi]^d$ consisting of exponential functions in connection to oversampling and nonuniform sampling of bandlimited functions. We derive a multidimensional nonuniform oversampling formula for…
We consider the problem of sampling from data defined on the nodes of a weighted graph, where the edge weights capture the data correlation structure. As shown recently, using spectral graph theory one can define a cut-off frequency for the…
In this paper, we provide a Graph Fourier Transform based approach to downsample signals on graphs. For bandlimited signals on a graph, a test is provided to identify whether signal reconstruction is possible from the given downsampled…
A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane $\mathbb{H}$ realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on…
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to…
When sampling multiple signals, the correlation between the signals can be exploited to reduce the overall number of samples. In this paper, we study the sampling theory of multiple correlated signals, using correlation to sample them at…
Sub-sampling can acquire directly a passband within a broad radio frequency (RF) range, avoiding down-conversion and low-phase-noise tunable local oscillation (LO). However, sub-sampling suffers from band folding and self-image…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
Sampling theory has benefited from a surge of research in recent years, due in part to the intense research in wavelet theory and the connections made between the two fields. In this survey we present several extensions of the Shannon…
This paper is concerned with the problem of reconstructing an infinite-dimensional signal from a limited number of linear measurements. In particular, we show that for binary measurements (modelled with Walsh functions and Hadamard…