Description: 1: An introduction to sampling theory1.1: General introduction1.2: Introduction - continued1.3: The seventeenth to the mid twentieth century - a brief review1.4: Interpolation and sampling from the seventeenth century to the mid twentieth century - a brief review1.5: Introduction - concluding remarks2: Background in Fourier analysis2.1: The Fourier Series2.2: The Fourier transform2.3: Poisson's summation formula2.4: Tempered distributions - some basic facts3: Hilbert spaces, bases and frames3.1: Bases for Banach and Hilbert spaces3.2: Riesz bases and unconditional bases3.3: Frames3.4: Reproducing kernel Hilbert spaces3.5: Direct sums of Hilbert spaces3.6: Sampling and reproducing kernels4: Finite sampling4.1: A general setting for finite sampling4.2: Sampling on the sphere5: From finite to infinite sampling series5.1: The change to infinite sampling series5.2: The Theorem of Hinsen and Klosters6: Bernstein and Paley-Weiner spaces6.1: Convolution and the cardinal series6.2: Sampling and entire functions of polynomial growth6.3: Paley-Weiner spaces6.4: The cardinal series for Paley-Weiner spaces6.5: The space ReH16.6: The ordinary Paley-Weiner space and its reproducing kernel6.7: A convergence principle for general Paley-Weiner spaces7: More about Paley-Weiner spaces7.1: Paley-Weiner theorems - a review7.2: Bases for Paley-Weiner spaces7.3: Operators on the Paley-Weiner space7.4: Oscillatory properties of Paley-Weiner functions8: Kramer's lemma8.1: Kramer's Lemma8.2: The Walsh sampling therem9: Contour integral methods9.1: The Paley-Weiner theorem9.2: Some formulae of analysis and their equivalence9.3: A general sampling theorem10: Ireggular sampling10.1: Sets of stable sampling, of interpolation and of uniqueness10.2: Irregular sampling at minimal rate10.3: Frames and over-sampling11: Errors and aliasing11.1: Errors11.2: The time jitter error11.3: The aliasing error12: Multi-channel sampling12.1: Single channel sampling12.3: Two channels13: Multi-band sampling13.1: Regular sampling13.2 Optimal regular sampling: 13.3: An algorithm for the optimal regular sampling rate13.4: Selectively tiled band regions13.5: Harmonic signals13.6: Band-ass sampling14: Multi-dimensional sampling14.1: Remarks on multi-dimensional Fourier analysis14.2: The rectangular case14.3: Regular multi-dimensional sampling15: Sampling and eigenvalue problems15.1: Preliminary facts15.2: Direct and inverse Sturm-Liouville problems15.3: Further types of eigenvalue problem - some examples16: Campbell's generalised sampling theorem16.1: L.L. Campbell's generalisation of the sampling theorem16.2: Band-limited functions16.3: Non band-limited functions - an example17: Modelling, uncertainty and stable sampling17.1: Remarks on signal modelling17.2: Energy concentration17.3: Prolate Spheroidal Wave functions17.4: The uncertainty principle of signal theory17.5: The Nyquist-Landau minimal sampling rate

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