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FIGURE 23.1 Description of some classes of signals: (a) continuous-time analog, (b) sampled-data, (c) digital
signal, (d) random signal.

FIGURE 23.2 Description of periodic signals: (a) CT, (b) DT.

to CT and DT signals are analog and digital signals, respectively. If the amplitude of a signal can take on
any value in a continuous range, then it is an analog signal. On the other hand, the amplitude of a digital
signal can have only finite number of values at discrete points. Examples of continuous-time, discrete-
time, digital, and random signals are shown in Fig. 23.1.
Deterministic signals fall into two main categories, namely periodic and aperiodic signals. A periodic
signal has the same values at times separated by one period, T, that is, x(t) satisfies the relation, x(t) =
x(t + T), −∞ < t < ∞. An example of a CT periodic signal is a sinusoidal waveform of the form x(t) = A
sin(Ωt + θ), where θ is the phase in radians, Ω = 2πF is the frequency in radians per second, and F is
the frequency in hertz. It should be noted that the frequency range for the analog sinusoids is −∞ < F < ∞.
A periodic DT signal is described by x(n) = x(n + N), −∞, < n < ∞, where N represents the period. An
example of this is the sinusoidal waveform x(n) = A sin(2πrn + θ), −∞ < n < ∞, where r is the signal
1
1
frequency per sample frequency and has values in the range − ≤ r ≤ . Samples of sinusoids having
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2 2
frequencies within this range are unique and distinct. However, DT sinusoids whose frequencies are
separated by an integer multiple of 2π are identical. Examples of analog and DT sinusoids are depicted
in Fig. 23.2.
Any deterministic signal that is not periodic is referred to as aperiodic or nonperiodic. Damped sinusoids
and exponential decaying signals are common examples of aperiodic signals. For some applications, it may
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