Classification of Signals - Signal Processing of Random Physiological Signals - page 13

3.1.1 Periodic vs. Nonperiodic Signals
Is the signal periodic or nonperiodic? A periodic signal is defined as a signal that repeats
the sequences of values exactly after a fixed length of time (the period, T ) as shown
in (3.1), such that

x ( t ) = x ( t + T ) for all t (3.1)

Keep in mind that a delay is written as a difference ( t − T ) in (3.2):

y ( t ) = x ( t − T ) (3.2)

The smallest positive T , which satisfies 3.1, is the period, which is the duration of one
complete cycle. The fundamental frequency ( f 0 ) of a periodic signal is defined as the
reciprocal of the period ( T ) as in (3.3):

1
T

f 0 = (3.3)

A nonperiodic signal or an “aperiodic” (almost periodic) signal does not have a
period ( T ). Typical nonperiodic signals include signals such as speech, electroencephalo-
grams (brainwaves) measured by surface electrodes, electromyogram, and respiratory
sounds.
From the standpoint of mathematical representation of signals, the periodic class
has the greatest theoretical importance. In most cases, an explicit mathematical expression
can be written for a periodic signal.

3.1.2 Random vs. Nonrandom Signals
Is the signal random or nonrandom (deterministic)? Another method of classifying
signals is whether or not the signal is random. The author's definition of a random signal
is a signal about which there is some degree of uncertainty before it actually occurs; that
is, “I've always considered a random signal as a time varying variable or function whose
magnitude varies erratically and in an unpredictable manner.”
The formal definition of a nonrandom signal is a signal that has no uncertainty
before it occurs. In other words, it is “ Deterministic ”; in most cases, an explicit math
expression can be written.