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Nonuniform Sampling and Multiscale Computation

Björn Engquist, Christina Frederick
2014 Multiscale Modeling & simulation  
The goal of this study is to establish the close relation between computational grids in multiscale modeling and sampling strategies developed in information theory.  ...  We prove that under certain band limiting conditions these multiscale functions can be uniquely and stably recovered from non-uniform samples of optimal rate.  ...  Nonuniform periodic sampling.  ... 
doi:10.1137/130936403 fatcat:4kox2ouajzfh3e7iehyknh4cle

Reconstruction of Nonuniformly Sampled Bandlimited Signals by Means of Time-Varying Discrete-Time FIR Filters

Håkan Johansson, Per Löwenborg
2006 EURASIP Journal on Advances in Signal Processing  
Furthermore, for an important special case, corresponding to periodic nonuniform sampling, it is shown that the reconstruction problem alternatively can be posed as a filter bank design problem, thus with  ...  The main theme of the paper is to show how a slight oversampling should be utilized for designing the reconstruction filters in a proper manner.  ...  class of periodic nonuniform sampling [2] as exemplified in Figure 1 (c).  ... 
doi:10.1155/asp/2006/64185 fatcat:wilpxhdqpfbtxeizd3pcw2l3ge

On High-Resolution Adaptive Sampling of Deterministic Signals [article]

Yehuda Dar, Alfred M. Bruckstein
2018 arXiv   pre-print
Specifically, we formulate solutions for the task of optimal high-resolution sampling, counterparts of well-known results for high-rate quantization.  ...  The second is a theoretical analysis of nonuniform sampling relevant to the emerging field of high-resolution signal processing.  ...  ACKNOWLEDGMENT The authors thank the reviewers for very pertinent and useful comments.  ... 
arXiv:1611.01850v4 fatcat:guxdyoy5sng2bbfdamx736clde

Intentionally patterned and spatially non-uniform film profiles in chemical vapor deposition processes

Raymond A. Adomaitis
2007 Surface & Coatings Technology  
Situations where it is desirable to control a chemical vapor deposition reactor to a spatially nonuniform film profile are presented in the context of a planetary reactor system for SiC CVD and a highly  ...  We focus on reactor designs and operation methods that enable deposition of spatially graded films for combinatorial studies, and on identifying and driving planetary CVD systems to a specific spatially  ...  The 6 response surface model coefficients b i , b i,4 , i = 1, 2, 3 are identified using a least squares procedure modified to enable computations with wafer class objects; a sequence of approximately  ... 
doi:10.1016/j.surfcoat.2007.04.117 fatcat:ssk62t2zojdtxdj5g3u7m4jldi

Data Sampling in Multidimensional NMR: Fundamentals and Strategies [chapter]

Mark W. Maciejewski, Mehdi Mobli, Adam D. Schuyler, Alan S. Stern, Jeffrey C. Hoch
2011 Topics in current chemistry  
In this chapter we review the fundamentals of uniform and nonuniform sampling methods in one and multidimensional NMR.  ...  Beginning with the introduction of Fourier Transform NMR by Ernst and Anderson in 1966, time domain measurement of the impulse response (the free induction decay) consisted of sampling the signal at a  ...  We thank Sven Hyberts for providing the Poisson gap sampling schedules used in Figure 8 , and for helpful discussions.  ... 
doi:10.1007/128_2011_185 pmid:21773916 pmcid:PMC6078388 fatcat:doi6np6k3raxtftzg6jveo4o74

Generating antialiased images at low sampling densities

Don P. Mitchell
1987 Proceedings of the 14th annual conference on Computer graphics and interactive techniques - SIGGRAPH '87  
An algorithm is presented for fast generation of nonuniform sampling patterns that are optimal in some sense. Some regions of an image may require extra sampling to avoid strong aliasing.  ...  The nonuniformity of the samples complicates this process, and a new nonuniform reconstruction filter is presented which solves this problem efficiently. This paper was presented in SIGGRAPH 87.  ...  Prefiltering has been done only approximately and for scenes built up from a restricted class of primitive objects.  ... 
doi:10.1145/37401.37410 dblp:conf/siggraph/Mitchell87 fatcat:blntrcefbfck5eb5hgksyltpmm

Generating antialiased images at low sampling densities

Don P. Mitchell
1987 Computer graphics  
An algorithm is presented for fast generation of nonuniform sampling patterns that are optimal in some sense. Some regions of an image may require extra sampling to avoid strong aliasing.  ...  The nonuniformity of the samples complicates this process, and a new nonuniform reconstruction filter is presented which solves this problem efficiently. This paper was presented in SIGGRAPH 87.  ...  Prefiltering has been done only approximately and for scenes built up from a restricted class of primitive objects.  ... 
doi:10.1145/37402.37410 fatcat:zvwviabujnarxofx6mmyhdhcla

Some Architectures for Chebyshev Interpolation [article]

Theja Tulabandhula
2010 arXiv   pre-print
Further, Chebyshev interpolation scheme is compared to the conventional equispaced interpolation vis-a-vis reconstruction error and relative number of samples.  ...  It is also shown that the use of a hybrid (or dual) Analog to Digital converter unit can reduce system power consumption by as much as 1/3rd of the original.  ...  For example, Runge (see [4] pp155-156) demonstrated that interpolation of equispaced signal values is non-optimal for a certain class of functions.  ... 
arXiv:1001.1185v1 fatcat:6xey6fuon5aophvgwdlejkf3ya

Spectral Analysis of Non-Uniformly Sampled Data: A New Approach Versus the Periodogram

Hao He, Jian Li, Petre Stoica
2009 2009 IEEE 13th Digital Signal Processing Workshop and 5th IEEE Signal Processing Education Workshop  
Then we go on to introduce a new enhanced method for spectral analysis of nonuniformly sampled data sequences.  ...  to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint.  ...  Ge for providing us with the measured radial velocity data used for extrasolar planet detection, and Dr. P. Tichavsky for his critical comments on a former version of this paper.  ... 
doi:10.1109/dsp.2009.4785952 fatcat:md7oztyfibguljulck7i4zxmxm

Spectral Analysis of Nonuniformly Sampled Data: A New Approach Versus the Periodogram

P. Stoica, Jian Li, Hao He
2009 IEEE Transactions on Signal Processing  
Then we go on to introduce a new enhanced method for spectral analysis of nonuniformly sampled data sequences.  ...  to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint.  ...  Ge for providing us with the measured radial velocity data used for extrasolar planet detection, and Dr. P. Tichavsky for his critical comments on a former version of this paper.  ... 
doi:10.1109/tsp.2008.2008973 fatcat:uchyqpjmirf7nlwy2etu7bdzze

Efficient Recovery of Sub-Nyquist Sampled Sparse Multi-Band Signals Using Reconfigurable Multi-Channel Analysis and Modulated Synthesis Filter Banks

Anu Kalidas M. Pillai, Hakan Johansson
2015 IEEE Transactions on Signal Processing  
Sub-Nyquist cyclic nonuniform sampling (CNUS) of a sparse multi-band signal generates a nonuniformly sampled signal.  ...  Assuming that the corresponding uniformly sampled signal satisfies the Nyquist sampling criterion, the sequence obtained via CNUS can be passed through a reconstructor to recover the missing uniform-grid  ...  Uniform sampling of x a (t) at a sampling frequency of f s = 1/T results in a discrete-time sequence x(n) = x a (nT ). Below, for the sake of simplicity, we assume that T = 1.  ... 
doi:10.1109/tsp.2015.2451104 fatcat:gzy7khy7pfdwzhdfhhcv4mmeom

CMOS compressed imaging by Random Convolution

L. Jacques, P. Vandergheynst, A. Bibet, V. Majidzadeh, A. Schmid, Y. Leblebici
2009 2009 IEEE International Conference on Acoustics, Speech and Signal Processing  
It acts as a convolutive filter on the imager focal plane, the current issued from each CMOS pixel undergoing a pseudo-random redirection controlled by each component of the filter sequence.  ...  The feasibility of the imager and its robustness under noise and non-linearities have been confirmed by computer simulations, as well as the reconstruction tools supporting the Compressed Sensing theory  ...  the decoder is non-linear and requires high computing power for real-time applications.  ... 
doi:10.1109/icassp.2009.4959783 dblp:conf/icassp/JacquesVBMSL09 fatcat:meyzrrohmfc2beniptdfdswx3u

Randomized nonuniform sampling and reconstruction in fractional Fourier domain

Liyun Xu, Feng Zhang, Ran Tao
2016 Signal Processing  
The nonuniform samples are treated as random perturbations from a uniform grid.  ...  The samples used for the sinc interpolation reconstruction are placed on another nonuniform grid which is not necessarily equal to the samples originally acquired.  ...  The nonuniform samples are regarded as random perturbations from a uniform sampling grid in the analysis. Therefore, the nonuniform sampling sequence has random characters.  ... 
doi:10.1016/j.sigpro.2015.09.016 fatcat:nu4mfnjqorcitbhsqc2c3fzfe4

Nonuniform sampling and non-Fourier signal processing methods in multidimensional NMR

Mehdi Mobli, Jeffrey C. Hoch
2014 Progress in nuclear magnetic resonance spectroscopy  
at a series of discrete intervals.  ...  concludes with a discussion of other approaches to speeding up data acquisition in NMR.  ...  Support from the US National Institutes of Health (GM102366, GM104517) and the Australian Research Council (DP140101098, FTl10100925) is gratefully acknowledged.  ... 
doi:10.1016/j.pnmrs.2014.09.002 pmid:25456315 pmcid:PMC5776146 fatcat:j4o6dqpoajd7rfspkkrd2mpylm

Sampling-50 years after Shannon

M. Unser
2000 Proceedings of the IEEE  
We then extend the standard sampling paradigm for a representation of functions in the more general class of "shift-invariant" functions spaces, including splines and wavelets.  ...  This paper presents an account of the current state of sampling, 50 years after Shannon's formulation of the sampling theorem. The emphasis is on regular sampling, where the grid is uniform.  ...  There is still room for optimization and design work in order to find the basis functions that give the best quality for a given computational budget (or support). V.  ... 
doi:10.1109/5.843002 fatcat:jm2pxi4xarakxe6fxja6ud4gje
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