Related papers: System Approximations and Generalized Measurements…
In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not…
In this paper we analyze the approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley-Wiener space $\mathcal{PW}_{\pi}^{1}$. It is known that there exist…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
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…
We show that a broad class of signal acquisition schemes can be interpreted as recording data from a signal $x$ in a space $\cal U$ (typically, though not exclusively, a space of bandlimited functions) via an orthogonal projection $w =…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a…
In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
We propose an adaptive non-uniform sampling framework for bandlimited signals based on an algorithm-encoder co-design perspective. By revisiting the convergence analysis of iterative reconstruction algorithms for non-uniform measurements,…
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…
In the field of signal processing, the sampling theorem plays a fundamental role for signal reconstruction as it bridges the gap between analog and digital signals. Following the celebrated Nyquist-Shannon sampling theorem, generalizing the…
In this note we study the problem of sampling and reconstructing signals which are assumed to lie on or close to one of several subspaces of a Hilbert space. Importantly, we here consider a very general setting in which we allow infinitely…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…
Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…
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…
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampling (GS) framework provides a robust methodology for…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling…