Biomedical Engineering Reference
In-Depth Information
signals are also commonly encountered in today's clinical setting. Unlike continu-
ous signals, which are defined along a continuum of points in space or time, discrete signals
are defined only at a subset of regularly spaced points in time and/or space. Discrete signals
are therefore represented by arrays or sequences of numbers. The notation,
Discrete
x
(
n
), is used to
represent a discrete sequence,
x
, that exists only at a subset of points in discrete time,
n
.Here,
n
¼
th element of the discrete sequence.
Although most biological signals are not discrete per se, discrete signals play an important role
due to today's advancements in digital technology. Sophisticated medical instruments are
commonly used to convert continuous signals from the human body to discrete digital
sequences (see Chapter 7) that can be analyzed and interpreted with a computer. Computer
axial tomography (CAT) scans, for instance, take digital samples from continuous x-ray images
of a patient that are obtained from different perspective angles (see Chapter 15). These digi-
tized or discrete image slices are then digitally enhanced, manipulated, and processed to
generate a full three-dimensional computer model of a patient's internal organs. Such technol-
ogies are indispensable tools for clinical diagnosis.
Biological signals can also be classified as being either
0, 1, 2, 3
...
is always an integer that represents the
n
deterministic
or
random
. Determin-
istic signals can be described by mathematical functions or rules.
transient
signals make up a subset of all deterministic signals. Periodic signals are usually composed
of the sum of different sine waves or sinusoid components and can be expressed as
Periodic
and
x
ð
t
Þ¼
x
ð
t
þ
kT
Þ
ð
11
:
1
Þ
where
is the period. The period represents the dis-
tance along the time axis between successive copies of the periodic signal. Periodic signals
have a basic waveshape with a duration of
x
(
t
) is the signal,
k
is an integer, and
T
units that repeats indefinitely. Transient
signals are nonzero or vary only over a finite time interval and subsequently decay to a con-
stant value as time progresses. The sine wave, shown in Figure 11.3a, is a simple example of
a periodic signal, since it repeats indefinitely with a repetition interval of 1 second. The
product of a decaying exponential and a sine wave, as shown in Figure 11.3b, is a transient
signal, since the signal amplitude approaches zero as time progresses.
Real biological signals almost always have some unpredictable noise or change in
parameters and, therefore, are not entirely deterministic. The ECG of a normal beating
heart at rest is an example of a signal that appears to be almost periodic but has a subtle
unpredictable component. The basic waveshape consists of the P wave, QRS complex,
and T wave and repeats (see Figure 3.22). However, the precise shapes of the P waves,
QRS complexes, and T are somewhat irregular from one heartbeat to another. The length
of time between QRS complexes, which is known as the R-R interval, also changes over
time as a result of heart rate variability (HRV). HRV is used as a diagnostic tool to predict
the health of a heart that has experienced a heart attack. The extended outlook for patients
with low HRV is generally worse than it is for patients with high HRV.
Random signals, also called
T
signals, contain uncertainty in the parameters that
describe them. Because of this uncertainty, mathematical functions cannot be used to precisely
describe random signals. Instead, random signals are most often analyzed using statistical
techniques that require the treatment of the random parameters of the signal with probability
distributions or simple statistical measures such as the mean and standard deviation. The elec-
tromyogram (EMG), an electrical recording of electrical activity in skeletal muscle that is
stochastic
