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In this thesis we present some fast algorithms for signal
processing problems which involve solving the close-to-
Toeplitz- plus-Hankel systems of equations. First, we review
the algorithm addressed by Hwang for the design of linear least
squares finite impulse response (FIR) filters with linear phase
characteristic. Then, based on this fast algorithm along with a
procedure recently proposed by Berberidis et al., we develop a
new fast algorithm for the modified covariance method. Both
these fast algorithms possess some desired features: (1) since
the inherent symmetry of the problems have been fully
expressed, both algorithms requires lower computational
complexity than other existing ones, (2) these new algorithms,
unlike other existing ones, involve only the order updates,
thus lending themselves to more efficient hardware
implementations. The extension to the unwindowed case and
adaptive filtering are also addressed in this thesis.
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