SIGNAL ANALYSIS USING NON-UNIFORM SAMPLING

Abstract

Uniform sampling is the dominant sampling scheme for most signal processing because its hardware implementation is relatively simple and allows for the utilization of efficient processing techniques, such as the fast Fourier transform. Uniform sampling is required to meet a minimum sampling rate constraint—called the Nyquist rate—to prevent aliasing in the frequency spectrum, which, in certain situations, can be impossible to meet. Non-uniform sampling and subsequent signal processing techniques can be used to recover the true frequency spectrum of a signal while sampling well under the Nyquist rate. Two processing techniques, called sequential component extraction and cross-interference coefficients matrix correction, can be applied to non-uniform sampling streams to provide spectral information. This thesis implements these techniques and identifies the conditions under which they can be applied successfully. The accuracy of both techniques was found to be dependent on the total number of samples of the signal, as opposed to uniform sampling, which is dependent on the sampling rate. Additionally, in a noise-free environment, with a sufficiently random non-uniform sampling stream, both techniques were able to accurately estimate signal spectrum characteristics with just a small number of samples as compared to the required number of samples for an equivalent uniform sampling process.