Biomedical Signal Processing - Computational Intelligence in Biomedical Engineering - page 68

Clearly, when γ = 1, the filter memory becomes infinite, or we obtain the
standard least squares method.
Although the RLS method is very ecient, there are problems with direct
implementation. If the reference noise signal r k is zero for some time, the
matrix P k will increase exponentially due to continuous division by γ , which
is less than unity. This no doubt causes overflow errors and further compu-
tational errors accumulate. The RLS method is also susceptible to computa-
tional roundoff errors, which can give a negative definite matrix P k at some
stage of the signal causing numerical instability since proper estimation of w
requires that P k be positive semidefinite. This cannot be guaranteed because
of the difference terms in the computation of P k , but the problem can be
alleviated by suitably factorizing the matrix P k to avoid explicit use of the
difference terms. Two such algorithms that give comparable accuracies to the
RLS algorithm are the square root (Ifeachor and Jervis, 1993) and upper
diagonal matrix factorization algorithms (Bierman, 1976).
2.8 Concluding Remarks
The signal-processing techniques reviewed in this chapter have been used
extensively to process biosignals. In the following chapters, we will investi-
gate how some of these techniques are employed, first to remove noise from
the signal and then to extract features containing discriminative information
from the raw biosignals. For pattern recognition applications, the coecients
of signal transforms have been commonly used to discriminate between classes.
In some cases, these coecients are sucient to fully characterize the signal
and classification can be easily achieved by setting single thresholds. Unfortu-
nately, in many other cases this is insucient and instead of spending too much
time obtaining fully separable features, we can employ CI techniques. These
techniques include advanced classifiers, which are better suited to handling
nonseparable data and dealing with nonlinear function estimations, topics
that form a major subject of Chapter 3.
References
Akaike, H. (1969). Power spectrum estimation through autoregression model
fitting. Annals of the Institute of Statistical Mathematics 21 , 407-449.
Akaike, H. (1974). A new look at the statistical model identification. IEEE
Transactions on Automatic Control 19 , 716-723.
Akay, M. (1994). Biomedical Signal Processing . San Diego, CA: Academic
Press.