  Analysing data that consists of one or more truncated exponential functions
is of great interest in a wide range of fields. Data consisting of one or more
exponential functions are measured by a wide range of instruments, examples
include: nuclear magnetic resonance, (NMR); magnetic resonance imaging (MRI);
the analysis of radioactive decay data; chromatography; lifetime fluorescence
imaging; spin resonance, (ESR). Many of the algorithms that are currently in
used for 'characterising' this data, are difficult to interpret or are they
useless and they produce erroneous results. Some of the key technical issues
associated with this problem are discussed in this article we also present some
results that use some elementary properties of exponential properties of
exponential and harmonic functions. These properties allow us to develop
relationships between these functions which we exploit to analyse exponentially
decaying signals in noisy environments
