Spectral analysis is typically used to identify structure, particularly 
harmonic components, in discrete stationary processes.  The raw spectrum 
estimate calculated by taking the Fourier Transform of the process is 
seriously biased by spectral leakage and is inconsistent.  The leakage 
stems from the fact that observed processes are finite in length.  The 
transform of a pure sinusoid, finite in length, is contaminated by subsidiary
peaks (leakage).  

Many techniques have been developed to minimise spectral leakage, one of the 
most recent and rigorously derived is Thomson's (1982) Multi-Taper Method (MTM).
Multiple orthogonal tapers which optimally minimise the spectral leakage are
applied to the process and the power spectrum calculated.  The tapers are the 
solutions to an eigenvalue problem, but code is readily available for their 
direct calculation in FORTRAN and MATLAB.  As the tapers are orthogonal the 
power spectra are independent, and can be averaged to give a consistent estimate
of the true spectrum with increased degrees of freedom.

The method will be introduced and compared to other bias reduction techniques 
by application to some one-dimensional simulated series.  It is then extended 
to two-dimensional processes and used to identify structure in temperature 
measurements taken on a regular grid over a square region.