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recorded biosignals using any combination of signal processing techniques that are
suitable for the particular application at hand [25]. In particular, the signal process-
ing reduces the dimensionality of the data space by extracting useful information or
“features” of the signal [29]. Thus, the high-dimensional recorded data is mapped
to a lower dimensional “feature space.” Moreover, the feature space is divided into
regions or “classes” in order to categorize each measured signal.
13.6.1 Features
Biosignals can be analyzed using a large set of signal processing methods. However,
some features are relatively simple to calculate while others are computationally
demanding. Moreover, the issue of computational complexity becomes particularly
important for integrated circuit implementations. Accordingly, Table 13.1 shows the
computational complexities of various useful features in terms of signal sample size
N
, filter order
n
, decomposition levels
L
(for wavelets), number of signals
m
(PCA),
lag
q
in terms of clock cycles, and the number of ALOPEX iterations
c
[29] (a blank
“-” where present indicates that no studies were found).
Table 13.1: Feature extraction methods
Method
Complexity
Parallel and/or pipelined
Mean
O
(
N
)
O
(
log
(
N
))
Variance
O
(
2
N
)
O
(
2log
(
N
))
FFT [124, 26]
O
(
N
log
(
N
))
O
(
log
(
N
))
n
2
LPC (Levinson) [33, 87]
O
(
nN
+
)
169 cycles/iteration
O
4
2
N
1
2
L
Wavelets (lifting) [93]
+
−
1
/
-
Karhunen-Loeve with ALOPEX [29]
O
(
2
cN
)
O
(
2
c
log
N
)
n
2
PCA - SGA [32]
Onm
O
(
)
O
(
Nq
2
+
3
qN
)
O
(
N
+
q
)
Third-order cumulant (skewness) [1]
N
6
-
a
The 169 clock cycles (actually 3,378 per 20 iterations) for a pipelined multiplier implementation
of the Levinson algorithm are reported in [136], however, there is no explicit mention of
complexity in that paper. It seems evident, however, that for
p
multipliers in parallel, a pipelined
Fourth-order cumulant (kurtosis) [96]
O
(
)
implementation of the Levinson algorithm would be
O
p
+
n
2
.Also,
O
(
L
4
)
is mentioned
in [141] for fourth-order moments.
13.6.2 Classifiers
When some features of measured neural activity contain useful information that can
be applied in regulating a stimulus generator, a method for automated classifica-
tion may be in order. To this end, there are various methods that can be employed
