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
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.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor or Philosophy of Loughborough University of Technology.