Previous article Next article Error-Free Recovery of Signals from Irregularly Spaced SamplesFrederick J. BeutlerFrederick J. Beutlerhttps://doi.org/10.1137/1008065PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. S. Black, Modulation Theory, Van Nostrand, New York, 1953 0089.20302 Google Scholar[2] J. L. Yen, On nonuniform sampling of bandwidth-limited signals, IRE Trans. Circuit Theory, CT-3 (1956), 251–257 CrossrefGoogle Scholar[3] Harold S. Shapiro and , Richard A. Silverman, Alias-free sampling of random noise, J. Soc. Indust. Appl. Math., 8 (1960), 225–248 10.1137/0108013 MR0121948 0121.14204 LinkISIGoogle Scholar[4] Frederick J. Beutler, Sampling theorems and bases in a Hilbert space, Information and Control, 4 (1961), 97–117 10.1016/S0019-9958(61)80001-6 MR0147315 0143.41704 CrossrefGoogle Scholar[5] H. P. Kramer, A generalized sampling theorem, Bull. Amer. Math. Soc., 63 (1957), 117–, Abstract Google Scholar[6] Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, v. 26, American Mathematical Society, New York, 1940viii+246 MR0003208 0145.08003 CrossrefGoogle Scholar[7] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963xiv+393 MR0157156 0111.06003 Google Scholar[8] Frigyes Riesz and , Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468 MR0071727 0070.10902 Google Scholar[9] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[10] Frederick J. Beutler and , Oscar A. Z. Leneman, The theory of stationary point processes, Acta Math., 116 (1966), 159–197 MR0199895 0147.16003 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Event-Driven Circuits and Systems: A Promising Low Power Technique for Intelligent Sensors in AIoT EraIEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 69, No. 7 | 1 Jul 2022 Cross Ref Random sampling for effective spectrum sensing in cognitive radio time slotted environmentPhysical Communication, Vol. 49 | 1 Dec 2021 Cross Ref Applications of the Hilbert Transform – A Nonparametric Method for Interpolation/Extrapolation of DataModern Characterization of Electromagnetic Systems and Its Associated Metrology | 13 August 2021 Cross Ref DASP Implementation of Continuous-Time, Finite-Impulse-Response Systems2020 28th European Signal Processing Conference (EUSIPCO) | 24 Jan 2021 Cross Ref Compressed encoding of vibration signals using extremum samplingSN Applied Sciences, Vol. 2, No. 7 | 22 June 2020 Cross Ref Level-crossing sampling: principles, circuits, and processing for healthcare applicationsCompressive Sensing in Healthcare | 1 Jan 2020 Cross Ref Representation and Reconstruction of Finite-Energy Band-Limited Signals via Pulse-Width ModulationIEEE Transactions on Signal Processing, Vol. 67, No. 19 | 1 Oct 2019 Cross Ref Preparing to launch: biologging reveals the dynamics of white shark breaching behaviourMarine Biology, Vol. 166, No. 7 | 22 June 2019 Cross Ref Use of Acceleration and Acoustics to Classify Behavior, Generate Time Budgets, and Evaluate Responses to Moonlight in Free-Ranging Snowshoe HaresFrontiers in Ecology and Evolution, Vol. 7 | 8 May 2019 Cross Ref A new synthesis approach for non-uniform filters in the log-scale: Proof of concept2019 5th International Conference on Event-Based Control, Communication, and Signal Processing (EBCCSP) | 1 May 2019 Cross Ref Assessing the effects of sampling frequency on behavioural classification of accelerometer dataJournal of Experimental Marine Biology and Ecology, Vol. 512 | 1 Mar 2019 Cross Ref A New Method for the Spectral Analysis of Unevenly Sampled Time SeriesImmunological Tolerance | 17 January 2019 Cross Ref Maximum Eigenvalue Based Detection Using Jittered Random Sampling2nd International Conference on Wireless Intelligent and Distributed Environment for Communication | 28 March 2019 Cross Ref A Novel Pulse Position Modulator for Compressive Data AcquisitionAdvances in Science, Technology and Engineering Systems Journal, Vol. 4, No. 1 | 1 January 2019 Cross Ref Signal recovery algorithm for 2-level amplitude sampling using chromatic signal approximationsSignal Processing, Vol. 153 | 1 Dec 2018 Cross Ref Analog-to-Digital Compression: A New Paradigm for Converting Signals to BitsIEEE Signal Processing Magazine, Vol. 35, No. 3 | 1 May 2018 Cross Ref Nonlinear time transformation-based vibration signal reconstruction for blade tip-timing under rotation speed fluctuations2017 Prognostics and System Health Management Conference (PHM-Harbin) | 1 Jul 2017 Cross Ref Recoverability of band-passed signals from non-zero threshold crossings2017 3rd International Conference on Event-Based Control, Communication and Signal Processing (EBCCSP) | 1 May 2017 Cross Ref Signal reconstruction from recurrent samples in fractional Fourier domain and its application in multichannel SARSignal Processing, Vol. 131 | 1 Feb 2017 Cross Ref An efficient non-uniform filtering method for level-crossing sampling2016 IEEE International Conference on Digital Signal Processing (DSP) | 1 Oct 2016 Cross Ref An error measurement for resampled level crossing signal2016 Second International Conference on Event-based Control, Communication, and Signal Processing (EBCCSP) | 1 Jun 2016 Cross Ref Truncated Physical Model for Dynamic Sensor Networks with Applications in High-Resolution Mobile Sensing and BIGDATAJournal of Engineering Mechanics, Vol. 142, No. 5 | 1 May 2016 Cross Ref Two Effective Approaches to Correct the Positioning Errors in a Spherical Near-Field–Far-Field TransformationElectromagnetics, Vol. 36, No. 2 | 22 February 2016 Cross Ref Event-Based Data Acquisition and Reconstruction—Mathematical BackgroundEvent-Based Control and Signal Processing | 2 December 2015 Cross Ref On convergence between natural and uniform sampling for PWM generation2015 49th Asilomar Conference on Signals, Systems and Computers | 1 Nov 2015 Cross Ref The Use of Acceleration to Code for Animal Behaviours; A Case Study in Free-Ranging Eurasian Beavers Castor fiberPLOS ONE, Vol. 10, No. 8 | 28 August 2015 Cross Ref Near-ideal causal smoothing filters for the real sequencesSignal Processing | 1 Jul 2015 Cross Ref An event driven technique for filtering computational complexity reduction2015 International Conference on Event-based Control, Communication, and Signal Processing (EBCCSP) | 1 Jun 2015 Cross Ref Reconstruction of periodic nonuniform samples using Lagrange interpolation in time-interleaved ADCsSignal, Image and Video Processing, Vol. 9, No. 2 | 9 April 2013 Cross Ref Energy Detection Approach for Spectrum Sensing in Cognitive Radio Systems with the Use of Random SamplingWireless Personal Communications, Vol. 79, No. 2 | 12 July 2014 Cross Ref Recovery of varying-bandwidth signal for level-crossing samplingProceedings of the 2014 IEEE Emerging Technology and Factory Automation (ETFA) | 1 Sep 2014 Cross Ref Calculation of Far-Field Radiation Pattern Using Nonuniformly Spaced Antennas by a Least Square MethodIEEE Transactions on Antennas and Propagation, Vol. 62, No. 4 | 1 Apr 2014 Cross Ref Adaptive rate filtering a computationally efficient signal processing approachSignal Processing, Vol. 94 | 1 Jan 2014 Cross Ref Sampling based on timing: Time encoding machines on shift-invariant subspacesApplied and Computational Harmonic Analysis, Vol. 36, No. 1 | 1 Jan 2014 Cross Ref Event-Driven Successive Charge Redistribution Schemes for Clockless Analog-to-Digital ConversionDesign, Modeling and Testing of Data Converters | 6 October 2013 Cross Ref Optimal representation of non-stationary random fields with finite numbers of samples: A linear MMSE frameworkDigital Signal Processing, Vol. 23, No. 5 | 1 Sep 2013 Cross Ref Turbulence phase screens based on polar-logarithmic spectral samplingApplied Optics, Vol. 52, No. 19 | 27 June 2013 Cross Ref Application of ADPW iterative algorithm for channel selection with the use of random sampling in software radio context2012 IEEE International Conference on Complex Systems (ICCS) | 1 Nov 2012 Cross Ref On sub-ideal causal smoothing filtersSignal Processing, Vol. 92, No. 1 | 1 Jan 2012 Cross Ref Democracy in action: Quantization, saturation, and compressive sensingApplied and Computational Harmonic Analysis, Vol. 31, No. 3 | 1 Nov 2011 Cross Ref An equivalent-time and clocked approach for continuous-time quantization2011 IEEE International Symposium of Circuits and Systems (ISCAS) | 1 May 2011 Cross Ref On the Prediction of a Class of Wide-Sense Stationary Random ProcessesIEEE Transactions on Signal Processing, Vol. 59, No. 1 | 1 Jan 2011 Cross Ref Event-driven data acquisition and continuous-time digital signal processingIEEE Custom Integrated Circuits Conference 2010 | 1 Sep 2010 Cross Ref Event-Driven Data Acquisition and Digital Signal Processing—A TutorialIEEE Transactions on Circuits and Systems II: Express Briefs, Vol. 57, No. 8 | 1 Aug 2010 Cross Ref Event-driven, continuous-time ADCs and DSPs for adapting power dissipation to signal activityProceedings of 2010 IEEE International Symposium on Circuits and Systems | 1 May 2010 Cross Ref Adaptive signal reconstruction for timing nonuniform of parallel sampling sys-temsJOURNAL OF ELECTRONIC MEASUREMENT AND INSTRUMENT, Vol. 24, No. 1 | 11 Mar 2010 Cross Ref Predictability on finite horizon for processes with exponential decrease of energy on higher frequenciesSignal Processing, Vol. 90, No. 2 | 1 Feb 2010 Cross Ref ON THE COMPENSATION OF PROBE POSITIONING ERRORS WHEN USING A NONREDUNDANT CYLINDRICAL NF-FF TRANSFORMATIONProgress In Electromagnetics Research B, Vol. 20 | 1 Jan 2010 Cross Ref Near-Field/Far-Field Transformation with Helicoidal Scanning from Irregularly Spaced DataInternational Journal of Antennas and Propagation, Vol. 2010 | 1 Jan 2010 Cross Ref Impulse-doublet sampling of random waveformsDigital Signal Processing, Vol. 19, No. 6 | 1 Dec 2009 Cross Ref Adaptive Rate Sampling and Filtering Based on Level Crossing SamplingEURASIP Journal on Advances in Signal Processing, Vol. 2009, No. 1 | 1 June 2009 Cross Ref Time-Interleaved Analog-to-Digital-Converter Compensation Using Multichannel FiltersIEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 56, No. 10 | 1 Oct 2009 Cross Ref Processing of signals using level-crossing sampling2009 IEEE International Symposium on Circuits and Systems | 1 May 2009 Cross Ref Non-uniform Sampling Schemes for RF Bandpass Sampling Receiver2009 International Conference on Signal Processing Systems | 1 Jan 2009 Cross Ref Functionally Weighted Lagrange Interpolation of Band-Limited Signals From Nonuniform SamplesIEEE Transactions on Signal Processing, Vol. 57, No. 1 | 1 Jan 2009 Cross Ref The predictability of band-limited, high-frequency and mixed processes in the presence of ideal low-pass filtersJournal of Physics A: Mathematical and Theoretical, Vol. 41, No. 38 | 22 August 2008 Cross Ref Reconstruction of Nonuniformly Sampled Bandlimited Signals Using a Differentiator–Multiplier CascadeIEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 55, No. 8 | 1 Sep 2008 Cross Ref Modeling the Nonlinear Properties of the <emphasis emphasistype="italic">in vitro</emphasis> Hippocampal Perforant Path-Dentate System Using Multielectrode Array TechnologyIEEE Transactions on Biomedical Engineering, Vol. 55, No. 2 | 1 Feb 2008 Cross Ref Downsampling Non-Uniformly Sampled DataEURASIP Journal on Advances in Signal Processing, Vol. 2008, No. 1 | 1 Jan 2008 Cross Ref A Novel Sampling Scheme for Efficient Analog to Digital ConversionSecond NASA/ESA Conference on Adaptive Hardware and Systems (AHS 2007) | 1 Aug 2007 Cross Ref New version of PLNoise: a package for exact numerical simulation of power-law noisesComputer Physics Communications, Vol. 177, No. 4 | 1 Aug 2007 Cross Ref Artifacts with uneven sampling of red noisePhysical Review E, Vol. 75, No. 1 | 23 January 2007 Cross Ref Adaptive Rate Filtering Fora Signal Driven Sampling Scheme2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07 | 1 Jan 2007 Cross Ref Spectral analysis of irregularly-sampled data: Paralleling the regularly-sampled data approachesDigital Signal Processing, Vol. 16, No. 6 | 1 Nov 2006 Cross Ref Sub-Nyquist Nonuniform Sampling and Perfect Reconstruction of Speech SignalsTENCON 2005 - 2005 IEEE Region 10 Conference | 1 Nov 2005 Cross Ref A Theoretical Exposition of Stationary Processes SamplingSampling Theory in Signal and Image Processing, Vol. 4, No. 3 | 1 September 2005 Cross Ref Hardware Implementation of a Broad-Band Vector Spectrum Analyzer Based on Randomized SamplingIEEE Transactions on Instrumentation and Measurement, Vol. 54, No. 4 | 1 Aug 2005 Cross Ref Asynchronous level crossing analog to digital convertersMeasurement, Vol. 37, No. 4 | 1 Jun 2005 Cross Ref Spectral analysis of nonuniformly spaced data using least square methodDigital Signal Processing, Vol. 15, No. 1 | 1 Jan 2005 Cross Ref A 120nm low power asynchronous ADCISLPED '05. Proceedings of the 2005 International Symposium on Low Power Electronics and Design, 2005. | 1 Jan 2005 Cross Ref Irregular Sampling of Generalized Harmonizable ProcessesStochastic Analysis and Applications, Vol. 22, No. 5 | 1 Jan 2004 Cross Ref Sparseness‐constrained least‐squares inversion: Application to seismic wave reconstructionGEOPHYSICS, Vol. 68, No. 5 | 1 Sep 2003 Cross Ref Antialiasing conditions in the delay-time Radon transformGeophysical Prospecting, Vol. 50, No. 6 | 18 November 2002 Cross Ref Random Topics in Nonuniform SamplingNonuniform Sampling | 1 Jan 2001 Cross Ref Filterbank reconstruction of bandlimited signals from nonuniform and generalized samplesIEEE Transactions on Signal Processing, Vol. 48, No. 10 | 1 Oct 2000 Cross Ref The predictability of continuous-time, bandlimited processesIEEE Transactions on Signal Processing, Vol. 48, No. 2 | 1 Feb 2000 Cross Ref A novel algorithm for computing autocorrelation of randomly sampled sequencesCircuits, Systems, and Signal Processing, Vol. 18, No. 6 | 1 Nov 1999 Cross Ref Minimum rate sampling and reconstruction of signals with arbitrary frequency supportIEEE Transactions on Information Theory, Vol. 45, No. 5 | 1 Jul 1999 Cross Ref Unambiguous signal recovery above the Nyquist using random‐sample‐interval imagingGEOPHYSICS, Vol. 63, No. 2 | 1 Mar 1998 Cross Ref 3D stacking of irregularly sampled data by wavefield reconstructionSEG Technical Program Expanded Abstracts 1997 | 22 March 2012 Cross Ref Sampling in a Hilbert spaceProceedings of the American Mathematical Society, Vol. 124, No. 12 | 1 January 1996 Cross Ref Unambiguous signal recovery above the Nyquist using random‐sample‐interval imaging (RSI) 2SEG Technical Program Expanded Abstracts 1996 | 22 March 2012 Cross Ref Evaluation of methods for assessing spectra from laser Doppler velocimetry signalsMeasurement, Vol. 15, No. 4 | 1 Jul 1995 Cross Ref Multiband signal reconstruction from finite samplesSignal Processing, Vol. 42, No. 3 | 1 Mar 1995 Cross Ref Reconstruction from unevenly spaced sampled data using the iterative methodsIEEE Transactions on Signal Processing, Vol. 43, No. 1 | 1 Jan 1995 Cross Ref Error analysis of the MMSE estimator for multidimensional band-limited extrapolations from finite samplesSignal Processing, Vol. 36, No. 1 | 1 Mar 1994 Cross Ref Interpolation of electromagnetic radiated fields over a plane by nonuniform samplesIEEE Transactions on Antennas and Propagation, Vol. 41, No. 11 | 1 Nov 1993 Cross Ref 3 Sampling of bandlimited signals: Fundamental results and some extensionsSignal Processing and its Applications | 1 Jan 1993 Cross Ref Analytic sampling of bandpass signalsSignal Processing, Vol. 29, No. 1 | 1 Oct 1992 Cross Ref Irregular sampling theorems and series expansions of band-limited functionsJournal of Mathematical Analysis and Applications, Vol. 167, No. 2 | 1 Jul 1992 Cross Ref Iterative Reconstruction of Multivariate Band-Limited Functions from Irregular Sampling ValuesSIAM Journal on Mathematical Analysis, Vol. 23, No. 1 | 1 August 2006AbstractPDF (2128 KB)Irregular Sampling and FramesWavelets | 1 Jan 1992 Cross Ref Deconvolution of two-dimensional images with zeros in the transfer functionApplied Optics, Vol. 30, No. 35 | 10 December 1991 Cross Ref Iterative and one-step reconstruction from nonuniform samples by convex projectionsJournal of the Optical Society of America A, Vol. 7, No. 3 | 1 March 1990 Cross Ref A New Approach to Irregular Sampling of Band-Limited FunctionsRecent Advances in Fourier Analysis and Its Applications | 1 Jan 1990 Cross Ref Messung der Übertragungseigenschaften einer hochauflösenden Farbkamera mit CCD-FlächensensorMustererkennung 1990 | 1 Jan 1990 Cross Ref A stable nonuniform sampling expansion involving derivativesIEEE Transactions on Information Theory, Vol. 35, No. 6 | 1 Nov 1989 Cross Ref Reconstruction of bounded signals from pseudo-periodic, irregularly spaced samplesSignal Processing, Vol. 17, No. 1 | 1 May 1989 Cross Ref On nonuniform sampling expansions using entire interpolating functions, and on the stability of Bessel-type sampling expansionsIEEE Transactions on Information Theory, Vol. 35, No. 3 | 1 May 1989 Cross Ref Reconstruction of two-dimensional signals from nonuniform samples or partial informationJournal of the Optical Society of America A, Vol. 6, No. 1 | 1 January 1989 Cross Ref The truncation error in the application of sampling series to electromagnetic problemsIEEE Transactions on Antennas and Propagation, Vol. 36, No. 7 | 1 Jul 1988 Cross Ref Image representation by zero and sine-wave crossingsJournal of the Optical Society of America A, Vol. 4, No. 11 | 1 November 1987 Cross Ref Nonuniform sampling techniques for antenna applicationsIEEE Transactions on Antennas and Propagation, Vol. 35, No. 3 | 1 Mar 1987 Cross Ref Approximate reconstruction of randomly sampled signalsSignal Processing, Vol. 12, No. 2 | 1 Mar 1987 Cross Ref Analysis of error in reconstruction of two-dimensional signals from irregularly spaced samplesIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 35, No. 2 | 1 Feb 1987 Cross Ref Reconstruction of Two-Dimensional Signals from Irregularly Spaced SamplesASST ’87 6. Aachener Symposium für Signaltheorie | 1 Jan 1987 Cross Ref Almost periodic extension of band-limited functions and its application to nonuniform samplingIEEE Transactions on Circuits and Systems, Vol. 33, No. 10 | 1 Oct 1986 Cross Ref Wavenumber support regions for arbitrary arraysCircuits, Systems, and Signal Processing, Vol. 4, No. 4 | 1 Dec 1985 Cross Ref A transformation method for the reconstruction of functions from nonuniformly spaced samplesIEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 33, No. 5 | 1 Oct 1985 Cross Ref Polynomial Interpolation of Randomly Sampled Bandlimited Functions and ProcessesSIAM Journal on Applied Mathematics, Vol. 42, No. 5 | 12 July 2006AbstractPDF (1424 KB)Time-limited sampling theorems for band-limited signals (Corresp.)IEEE Transactions on Information Theory, Vol. 28, No. 5 | 1 Sep 1982 Cross Ref A new sampling theorem based on the minimum energy principleElectronics and Communications in Japan (Part I: Communications), Vol. 64, No. 3 | 1 Mar 1981 Cross Ref Data reduction of sampled speech signals: method and resultsInternational Journal of Electronics, Vol. 46, No. 4 | 16 January 2007 Cross Ref A property of random processes with unit multiplicityJournal of Multivariate Analysis, Vol. 7, No. 4 | 1 Dec 1977 Cross Ref The Shannon sampling theorem&#8212;Its various extensions and applications: A tutorial reviewProceedings of the IEEE, Vol. 65, No. 11 | 1 Nov 1977 Cross Ref A sampling theorem for irregularly spaced sample points (Corresp.)IEEE Transactions on Information Theory, Vol. 22, No. 5 | 1 Sep 1976 Cross Ref Estimation of the mean of a stationary time series by samplingJournal of Applied Probability, Vol. 10, No. 02 | 14 July 2016 Cross Ref Estimation of the mean of a stationary time series by samplingJournal of Applied Probability, Vol. 10, No. 2 | 14 July 2016 Cross Ref Uniform linear prediction of bandlimited processes from past samples (Corresp.)IEEE Transactions on Information Theory, Vol. 18, No. 5 | 1 Sep 1972 Cross Ref Alias-free randomly timed sampling of stochastic processesIEEE Transactions on Information Theory, Vol. 16, No. 2 | 1 Mar 1970 Cross Ref Fourier transform for non-uniformly sampled data in the study of systematic errors in common-view time transferProceedings of the 1998 IEEE International Frequency Control Symposium (Cat. No.98CH36165) Cross Ref A new class of asynchronous A/D converters based on time quantizationNinth International Symposium on Asynchronous Circuits and Systems, 2003. Proceedings. Cross Ref Signal recovery in time-interleaved analog-to-digital converters2004 IEEE International Conference on Acoustics, Speech, and Signal Processing Cross Ref Optimal estimation of subband speech from nonuniform non-recurrent signal-driven sparse samples2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221) Cross Ref A Level-Crossing Flash Asynchronous Analog-to-Digital Converter12th IEEE International Symposium on Asynchronous Circuits and Systems (ASYNC'06) Cross Ref Hardware implementation of a broad-band vector spectrum analyzer based on randomized samplingProceedings of the 21st IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.04CH37510) Cross Ref Spectral analysis of nonuniformly sampled data using a least square method for application in multiple PRF systemProceedings 2000 IEEE International Conference on Phased Array Systems and Technology (Cat. No.00TH8510) Cross Ref Optimum sampling for estimation of Fourier coefficients in noiseICASSP '81. IEEE International Conference on Acoustics, Speech, and Signal Processing Cross Ref Irregular sampling theory and scattered-center radial Gaussian networks[1992] Proceedings of the 31st IEEE Conference on Decision and Control Cross Ref Sub-Nyquist nonuniform sampling and perfect reconstruction of signalsProceedings of 2004 International Symposium on Intelligent Signal Processing and Communication Systems, 2004. ISPACS 2004. Cross Ref Voice and image recovery from lost samples1991., IEEE International Sympoisum on Circuits and Systems Cross Ref Determination of the aliasing band corresponding to each spectrum peak in ocean-bottom temperature spectraJournal of Geophysical Research, Vol. 74, No. 23 | 20 September 2012 Cross Ref Image degradation in undersampled hologramsPhysics Letters A, Vol. 28, No. 9 | 1 Feb 1969 Cross Ref Volume 8, Issue 3| 1966SIAM Review277-426 History Submitted:22 September 1965Published online:18 July 2006 InformationCopyright © 1966 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1008065Article page range:pp. 328-335ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics