An introduction to sampling theory / 1: |
General introduction / 1.1: |
Introduction - continued / 1.2: |
The seventeenth to the mid twentieth century - a brief review / 1.3: |
Interpolation and sampling from the seventeenth century to the mid twentieth century - a brief review / 1.4: |
Introduction - concluding remarks / 1.5: |
Background in Fourier analysis / 2: |
The Fourier Series / 2.1: |
The Fourier transform / 2.2: |
Poisson's summation formula / 2.3: |
Tempered distributions - some basic facts / 2.4: |
Hilbert spaces, bases and frames / 3: |
Bases for Banach and Hilbert spaces / 3.1: |
Riesz bases and unconditional bases / 3.2: |
Frames / 3.3: |
Reproducing kernel Hilbert spaces / 3.4: |
Direct sums of Hilbert spaces / 3.5: |
Sampling and reproducing kernels / 3.6: |
Finite sampling / 4: |
A general setting for finite sampling / 4.1: |
Sampling on the sphere / 4.2: |
From finite to infinite sampling series / 5: |
The change to infinite sampling series / 5.1: |
The Theorem of Hinsen and Kloosters / 5.2: |
Bernstein and Paley-Weiner spaces / 6: |
Convolution and the cardinal series / 6.1: |
Sampling and entire functions of polynomial growth / 6.2: |
Paley-Weiner spaces / 6.3: |
The cardinal series for Paley-Weiner spaces / 6.4: |
The space ReH1 / 6.5: |
The ordinary Paley-Weiner space and its reproducing kernel / 6.6: |
A convergence principle for general Paley-Weiner spaces / 6.7: |
More about Paley-Weiner spaces / 7: |
Paley-Weiner theorems - a review / 7.1: |
Bases for Paley-Weiner spaces / 7.2: |
Operators on the Paley-Weiner space / 7.3: |
Oscillatory properties of Paley-Weiner functions / 7.4: |
Kramer's lemma / 8: |
Kramer's Lemma / 8.1: |
The Walsh sampling therem / 8.2: |
Contour integral methods / 9: |
The Paley-Weiner theorem / 9.1: |
Some formulae of analysis and their equivalence / 9.2: |
A general sampling theorem / 9.3: |
Irregular sampling / 10: |
Sets of stable sampling, of interpolation and of uniqueness / 10.1: |
Irregular sampling at minimal rate / 10.2: |
Frames and over-sampling / 10.3: |
Errors and aliasing / 11: |
Errors / 11.1: |
The time jitter error / 11.2: |
The aliasing error / 11.3: |
Multi-channel sampling / 12: |
Single channel sampling / 12.1: |
Two channels / 12.3: |
Multi-band sampling / 13: |
Regular sampling / 13.1: |
Optimal regular sampling / 13.2: |
An algorithm for the optimal regular sampling rate / 13.3: |
Selectively tiled band regions / 13.4: |
Harmonic signals / 13.5: |
Band-ass sampling / 13.6: |
Multi-dimensional sampling / 14: |
Remarks on multi-dimensional Fourier analysis / 14.1: |
The rectangular case / 14.2: |
Regular multi-dimensional sampling / 14.3: |
Sampling and eigenvalue problems / 15: |
Preliminary facts / 15.1: |
Direct and inverse Sturm-Liouville problems / 15.2: |
Further types of eigenvalue problem - some examples / 15.3: |
Campbell's generalised sampling theorem / 16: |
L.L. Campbell's generalisation of the sampling theorem / 16.1: |
Band-limited functions / 16.2: |
Non band-limited functions - an example / 16.3: |
Modelling, uncertainty and stable sampling / 17: |
Remarks on signal modelling / 17.1: |
Energy concentration / 17.2: |
Prolate Spheroidal Wave functions / 17.3: |
The uncertainty principle of signal theory / 17.4: |
The Nyquist-Landau minimal sampling rate / 17.5: |
An introduction to sampling theory / 1: |
General introduction / 1.1: |
Introduction - continued / 1.2: |