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Constructing Tight Gabor Frames Using CAZAC Sequences
The construction of finite tight Gabor frames plays an important role in many applications. These applications include significant ones in signal and...
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Stability and Robustness of RBF Interpolation
This article considers how some methods of uniform and nonuni-form interpolation by translates of radial basis functions — focusing on the case of...
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Reconstruction from Periodic Nonstationary Sampling (PNS) without Resampling
Periodic Nonuniform Samplings (PNS) are concatenations of periodic samplings of same periods but which are shifted. They allow to suppress aliasings,...
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Sampling with Derivatives in the Bergman Space
We characterize sets of sampling for Bergman space functions and their derivatives. In particular, we show that the methods used in the setting of...
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Graph Theoretic Uncertainty and Feasibility
We expand upon a graph theoretic set of uncertainty principles with tight bounds for difference estimators acting simultaneously in the graph domain...
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Strong Divergence of Approximation Processes in Banach Spaces
In this paper we analyze the divergence behavior of linear approximation processes in general Banach spaces. If the approximation process is given by...
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Separation of Zeros, a Hermite Interpolation Based and a Frame Based Reconstruction Algorithms for Bandlimited Functions
It is shown that if a non-zero function f ∈ B σ has infinitely many double zeros on the real axis, then there exists at least one pair of consecutive...
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Nonuniform Sampling, Reproducing Kernels, and the Associated Hilbert Spaces
In a general context of positive definite kernels k , we develop tools and algorithms for sampling in reproducing kernel Hilbert space ℋ (RKHS). With...
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Classical Sampling Series of Band Limited Functions: Oversampling and Non-existence
Growth conditions are given on the samples f ( n ), n = 0 , ± 1, ± 2, … , of an entire function f ( z ) of exponential type less than π that imply that the...
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Evaluation of a Class of Quadratic Gauss Sums by Sampling a Continuous Chirp Signal
The calculation of Discrete Fourier Transform (DFT) of a periodic discrete-time chirp ends in the evaluation of a quadratic Gauss sum. The...
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Frame Expansions of Bandlimited Signals Using Prolate Spheroidal Wave Functions
We consider methods to compute duals of frames for Paley–Wiener spaces generated by shifts of certain prolate spheroidal wave functions. In...
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Krylov Subspace Methods in Dynamical Sampling
Let B be an unknown linear evolution process on ℂ d ≃ ℓ 2 ( ℤ d ) driving an unknown initial state x and producing the states { B ℓ x, ℓ = 0,1 ,… } at...
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On the Dual Frame Induced by an Invertible Frame Multiplier
Recently it has been established that given an invertible frame multiplier with semi-normalized symbol, a specific dual of any of the two involved...
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Filters and Matrix Factorization
We give a number of explicit matrix-algorithms for analysis/synthesis in multi-phase filtering; i.e., the operation on discrete-time signals which...
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Consistent Sampling for Multi Frame Generators with Distinct Sampling Rates
We consider a general sampling and reconstruction process in the space L 2 (R). For any input signal f from L 2 (R), we take y ield the same generalized...
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Multidimensional Signal Recovery in Discrete Evolution Systems via Spatiotemporal Trade Off
The problem of recovering an evolving signal from a set of samples taken at different time instances, has been well-studied for one-variable signals...
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Design Tools for Random Sampling in Multistandard Radio Signal Processing
This paper proposes new extensions to random sampling analytical formulations suitable for radio signal spectral analysis. A Fourier transform...
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Converse Sampling and Interpolation
The present note focuses on ideas of converse sampling and related ideas of interpolation. The presentation is in the setting of reproducing kernel...
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Sampling Formulas for Groups of Operators in Banach Spaces
We extend some results about sampling of entire functions of exponential type to Banach spaces. By using the generator D of a one-parameter group e tD ...