The aim of this thesis is the development and implementation of
efficient affine projection algorithms for multichannel active
noise control. Different approaches to this issue have been
considered. First of all, various efficient affine projection
algorithms have been developed; a specific software allows to
validate by simulation the presented algorithms, and finally, the
performance of the adaptive controllers considered have been
validated in a real practical system by measurement of the
acoustical sensation inside an enclosure.

In recent years, affine projection algorithms have been proposed
for adaptive system applications as an efficient alternative to
the slow convergence speed of least mean square (LMS) type
algorithms, showing, then, good performance, robustness and
stability. These algorithms update the weights based, instead of
on the current input vector (as the NLMS algorithm), on N
previous input vectors, being N the projection order. For
that reason, the affine projection algorithm can be consider as a
NLMS extension. Whereas much attention has been focused on the
development of efficient versions of affine projection algorithms
for echo cancellation applications, the similar adaptive problem
presented by active noise control (ANC) systems has not been
studied so deeply. This work is focused on the necessity to reduce
even more the computational complexity of affine projection
algorithms for real-time ANC applications. We present some
alternative efficient versions of existing affine projection
algorithms that do not significantly degrade performance in
practice. Furthermore, while in the ANC context the commonly used
affine projection algorithm is based on the modified filtered-x
structure, an efficient affine projection algorithm based on the
(non-modified) conventional filtered-x structure, as well as
efficient methods to reduce its computational burden, are
discussed and analyzed throughout this thesis. Although the
modified filtered-x scheme exhibits better convergence speed than
the conventional filtered-x structure and allows recovery of all
the signals needed in the affine projection algorithm for ANC, the
conventional filtered-x scheme provides a significant
computational saving, avoiding the additional filtering needed by
the modified filtered-x structure. In this work, it is shown that
the proposed efficient versions of affine projection algorithms
based on the conventional filtered-x structure show good
performance, comparable to the performance exhibited by the
efficient approaches of modified filtered-x affine projection
algorithms, and also achieve meaningful computational savings.

The commented points will be studied by means of the following
experiment and analysis:
_ Development of the multichannel affine projection algorithms
for active noise control based on the conventional filtered-x
structure and on the modified structure. Moreover, different
efficient strategies for the affine projection algorithms have
been studied. Finally, a theoretical study of the steady-state
mean square error of the affine projection algorithms will be
carried out. 
_ Simulation results have been obtained. For this
purpose, a software has been specifically designed to validate the
developed algorithms. 
_ Finally, the ability of the affine
projection algorithms to reduce the sound field in a multichannel
ANC system has been evaluated by means of a real practical
implementation.