Biomedical Engineering Signal Analysis - Signal Processing of Random Physiological Signals - page 3

Many systems cannot be analyzed as a whole because of the enormous complexity of the
systems and the lack of a satisfactory mathematical model or models for the systemwide
component; for example, large systems such as an aircraft, spacecraft, etc. Subsystems can
be treated and studied independently: the body, brain, central nervous system, endocrine
system, etc.
To study and analyze a system properly, the means by which energy is prop-
agated through the system must be studied. Evaluation of energy within a system is
done by specifying how varying qualities change as a function of time within the sys-
tem. A varying quantity is referred to as a signal . Signals measure the excitation and
responses of systems and are indispensable in describing the interaction among vari-
ous components/subsystems. Complicated systems have multi-inputs and multioutputs,
which do not necessarily have to be of the same number. Signals also carry information
and coding (i.e., encoded messages), which has led to the field of signal theory in com-
munication systems. Systems analysis is used to find the response to a specific input or
range of inputs when

1) the system does not exist and is possible only as a mathematical model;

2) experimental evaluation of a system is more difficult and expensive than ana-

lytical studies (i.e., ejection from an airplane, automobile crash, forces on lower
back); and

3) study of systems under conditions too dangerous for actual experimentation (i.e.,

a/c ejection, severe weather conditions).

System representation is performed by means of specifying relationships among the
systems variables, which can be given in various forms, for example, graphs, tabular val-
ues, differential equations, difference equations, or combinations. We will be concerned
primarily with the system representation in terms of ordinary linear differential equations
with constant coefficients.