Martin, Richard James; (1998) Irregularly sampled signals: Theories and techniques for analysis. Doctoral thesis (Ph.D.), University College London (United Kingdom).

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Abstract

This thesis is about sampling theory and methods for analysing signals that have been sampled at irregularly spaced points. Irregular sampling may arise naturally (examples of its occurrence may be found in geophysics, tomography, astronomy, and laser anemometry). In many cases it presents difficulties because standard techniques are unable to cope with the uneven sampling. However there is an alternative and exciting facet to the subject: deliberate aperiodic sampling. This is being mooted as a method for unambiguous frequency identification in new generations of signal analysers and of pulse-Doppler and synthetic-aperture radars. For the classes of signal that these systems need to process and analyse, signal reconstruction is not of prime importance and it can be the wrong approach. The principal aim of this thesis is to develop methods for analysing irregularly sampled data and the principal theme is methods that do not employ explicit signal reconstruction. The key contributions of this thesis are the development of prediction and filtering. A difficult problem associated with the spectral analysis of irregularly sampled signals is that the dynamic range of the observed spectrum is greatly reduced. It can however be resolved using a combination of elementary spectral analysis and advanced linear filtering techniques. The fast optimal filtering algorithms enable this to be done. They are derived using our general theory of linear prediction, which we extensively test on synthetic data. Other important contributions are made in the theories of nonlinear prediction and of sampling series. Nonlinear techniques are designed for signals of dynamical origin and we show that they can be made to work for irregular sampling. The work on sampling series shows that classical signal processing techniques such as system identification, convolution and filtering are not the preserve of regular sampling. Additionally an extensive review of sampling theory and its relation to signal processing is included. It provides an in-depth introduction to the subject and its fascinating literature.

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