3.6.3 Components:
General Mathematics and Statistics
The mathematics components allow users to program new capabilities
from a set of building blocks that include basic operators
(e.g., addition, subtraction) and trigonometric functions
(e.g., exponentiation, logarithms). The statistics components
allow computation of standard statistical measures such as mean
and variance. The latter are more difficult to program because they
require a long-term view of the signal.
Four basic components are reviewed here:
-
Calculus:
includes the differentiation operation that
has been previously used to generate delta and delta-delta
features.
-
Constant:
allows a mechanism for applying global constants,
such as the mean value of a signal, to a signal. This class is used
extensively to implement algorithms requiring mult-pass processing.
-
Math:
provides an ability to form weighted linear combinations
of functions of feature vectors. This class is designed to provide
maximum flexibility by supporting a mini-scripting language for
functional analysis. It gives the front end a Matlab-like capability.
-
Statistics:
used to compute means, variances, min, max, and
other global measures of the inputs. This class is used to implement
concepts such a mean normalization and variance-weighting. Since
this class accumulates global values of its inputs, its interface
is a little more complicated. Most statistical computations are
inherently non-real-time, and require at least one complete pass
over the data.
More details on our mathematical and statistical operators
are described in our
workshop notes on signal processing.
We also have several
laboratory exercises
available to teach you how to program with the algorithm classes.
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