Signals and systems - Biomedical Engineering Desk Reference - page 65

signal is referred to as an analog signal. For example, the
temperature in a room can be encoded so that 0 V rep-
resents 0.0 C, 5 V represents 10 C, 10 V represents
20 C, and so on, so that the encoding equation for
temperature would be as follows:
Temperature ¼ 2 Voltage amplitude
Analog encoding is common in consumer electronics such
as high-fidelity amplifiers and television receivers, although
many applications that traditionally used analog encoding,
such as sound and video recording, now use discrete or
digital encoding. Nonetheless, analog encoding is likely to
remain important to the biomedical engineer, if only be-
cause many physiological systems use analog encoding, and
most biotransducers generate analog-encoded signals.
The typical analog signal is one whose amplitude varies
in time as follows:

language used throughout this text also uses brackets in
a different context.} Because digital numbers can only
represent discrete or specific amplitudes, the analog signal
must also be sliced up in amplitude. Hence, to digitize an
analog signal requires slicing the signal in two ways: in time
and in amplitude.
Slicing the signal into discrete points in time is termed
time sampling or simply sampling. Time slicing samples
the continuous waveform, x ( t ), at discrete prints in time,
nT s , where T s is the sample interval. Slicing the signal
amplitude in discrete levels is termed quantization
( Figure 2.3-4 ). The equivalent number can only ap-
proximate the level of the analog signal, and the degree of
approximation will depend on the range of binary num-
bers and the amplitude of the analog signal. For example,
if the signal is converted into an 8-bit binary number, this
number is capable of 2 8 or 256 discrete values. If the
analog signal amplitude ranges between 0.0 and 5.0 V, the
quantization interval in volts will be 5/256 or 0.019 V. If,
as is usually the case, the analog signal is time varying in
a continuous manner, it must be approximated by a series
of binary numbers representing the approximate analog
signal level at discrete points in time ( Figure 2.3-4 ).

xðtÞ¼fðtÞ

[Eq. 2.3.1]

When a continuous analog signal is converted to the
digital domain, it is represented by a series of numbers
that are discrete samples of the analog signals at a specific
point in time:

X½n¼x½ 1 ; x½ 2 ; x½ 3 ; . ; x½n [Eq. 2.3.2]

Example 2.3.1: A 12-bit analog-to-digital converter
(ADC) advertises an accuracy of the least significant
bit (LSB). If the input range of the ADC is 0 to 10 V,
what is the resolution of the ADC in analog volts?
Solution: If the input range were 10 V, the analog voltage
represented by the LSB would be as follows:

Usually this series of numbers would be stored in se-
quential memory locations with x 1 followed by x 2 , then
x 3 , and so forth. {It is common to use brackets to identify
a

discrete variable (i.e., x [ n ]); but note that the

MATLAB (MathWorks, Natick, MA) programming

Figure 2.3-4 Digitizing a continuous signal (upper left) requires slicing the signal in time and amplitude (right side). The result is a series of
discrete numbers (x's) that approximate the original signal, and the resultant digitized signal (lower left) consists of a series of discrete
steps in time and value.