Biomedical Signal Processing - Computational Intelligence in Biomedical Engineering - page 62

A combination of low-pass and high-pass integer filters can be used to design
a bandpass integer filter. This filter shares characteristics of basic integer filters
in that the transfer function coecients are limited to integers, although the
poles can only be placed at θ =60 ◦ , 90 ◦ , and 120 ◦ . The sampling frequency
must be selected so that the passband exists between these three angular
locations. As before, the complex conjugate poles (1 + z −m ) and (1

z −m ) are
used to cancel the zeroes in the passband frequency. It should be noted that
as the number of zeroes is increased, the bandwidth decreases, the amplitude
of the side lobes decreases, cutoff steepness increases, and more sample data
must be stored to compute the difference equations.

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2.7 Adaptive Filters
In some biomedical applications, such as EEG and EMG monitoring, the
noise is much greater than the intended signal to be measured. This problem
is further exacerbated by the fact that both required signal and noise coexist
in the same frequency band and so the noise cannot be selectively filtered out
by removing any particular frequency band. In this situation, fixed coecient
filters cannot be used because they would filter out the required signal. In
extreme cases, the frequency band in which the noise exists also varies within
the band of the required signal. Clearly in such cases, we require a filter that
can adjust or adapt to the changing noise.
Adaptive filters are generalized filters with filter coecients not specified
prior to operation but change during the operation in an intelligent manner
by adapting to the incoming signal. This is accomplished by using adaptive
algorithms such as least mean squares (LMS), recursive least squares (RLS),
and Kalman filter-type algorithms. We will review the general adaptive fil-
ter and two popular and straightforward adaptive algorithms, namely, the
LMS method and the RLS method. The LMS method is preferred due to its
stability, but the RLS method has been shown to have superior convergence
properties. Kalman filter algorithms occupy a large part of the literature and
are well described in references such as Brown (1997), Banks (1990), and
Clarkson (1993).

2.7.1 General Adaptive Filter
Adaptive filtering begins with a general filter, which usually has a FIR struc-
ture. Other forms such as the IIR or lattice structures can be used (Ifeachor
and Jervis, 1993), but the FIR structure as shown in Figure 2.21 is more
stable and easily implemented. There are two main components to the filter,
the filter coecients, which are variable and the adaptive algorithm used to
change these coecients.