Digital spectral analysis using unconventional sampling methods

The work presented in this thesis covers the design of various sampling/ processing schemes which allow the capabilities of a digital spectral analysis system to be extended to cope with specific spectral analysis applications where sampling rates are restricted. It is shown how the sampling/processing methods can be tailored to suit various types of signals so as to minimise the sampling rate. Uniform sampling of multiple narrowband signals is the first specialised sampling technique to be discussed. Here sampling rate reductions are devised by employing spectral band interlacing which is similar in principle to the classical case of sampling a single narrowband signal but on a much more complicated level. Periodic staggered sampling is also considered with application to the sampling of multiple bandlimited signals. It is shown that such a sampling technique can be constructed with a mean sampling rate equal to the occupied frequency space of the signal, yet be insensitive to the signals frequency distribution of energy from the point of view of reconstruction ambiguity. To cover the spectral analysis of random signals a general resume is given to both statistical and random sampling techniques in the estimation of the power spectral density of stationary random waveforms. Statistical sampling is put forward as an unconventional way of digital spectral analysis in an attempt to break the "engineering" approach of uniform time sampling. Random sampling is suggested as a way of reducing the sampling rate for spectral analysis of stochastic waveforms but problems with spectral noise levels were encountered. A new approach to autocorrelation estimation is then given in an attempt to combat the defficiencies of random sampling but to maintain sampling rates as low as possible. The sampling/processing techniques involved with this new method are again based on a staggered periodic sampling waveform but of a specially designed staggered pattern. The thesis finishes with a short description of the practical problem of measuring turbine blade vibrations using blade-tip displacement detection. Suggestions are given as to the use of two of the data processing methods which are based on periodic staggered sampling. It is shown possible to use these two processing techniques in parallel while operating on a common source of data samples and giving separate output spectral analyses on different constituent vibrations present on the turbine blading.