Signal Classifications

This page is © Dec 5, 2013 Melissa Selik, Richard Baraniuk, Michael Haag and is licensed under a Creative Commons Attribution License 3.0 license.

The info below lays out some of the fundamentals of signal classifications. This is bascially a list of definitions and properties that are fundamental to the discussion of signals and systems.

Continuous-Time vs. Discrete-Time

As the names suggest, this classification is determined by whether or not the time axis (x-axis) is discrete (countable) or continuous (see figure 1).  A continuous-time signal will contain a value for all real numbers along the time axis.

In contrast to this, a discrete-time signal is often created by using the sampling theorem to sample a continuous signal, so it will only have values at equally spaced intervals along the time axis.

Continuous vs Discrete
Figure 1. Continuous vs. Discrete time signals

Analog vs. Digital

The difference between analog and digital is similar to the difference between  continuous-time and discrete-time.  In this case, however, the difference is with respect to the value of the function (y-axis) (figure 2).  Analog corresponds to a continuous y-axis, while digital corresponds to a discrete y-axis.  An easy example of a digital signal is a binary sequence, where the values of the function can only be one or zero.

Figure 2. Analog vs Digital Signal

Periodic vs. Aperiodic

Periodic signals repeat with some period T (figure 3), while aperiodic, or nonperiodic, signals do not (figure 4).  We can define a periodic function through the following mathematical expression, where t can be any number and T is a positive constant:

f(t) = f(t+T)

The fundamental period of our function f(t), is the smallest value of T that still allows the above equation to be true.

periodic signal
Figure 3. Periodic Signal
aperiodic signal
Figure 4. Aperiodic Signal

Deterministic vs. Random

A deterministic signal is a signal in which each value of the signal is fixed and can be determined by a mathematical expression, rule, or table. Because of this, the future values of the signal can be calculated from past values with complete confidence (figure 5). On the other hand, a random signal has a lot of uncertainty about its behavior. The future values of a random signal cannot be accurately predicted and can usually only be guessed based on the averages of sets of signals (figure 6).

Deterministic Signal
Figure 5. Deterministic Signal
Random Signal
Figure 6. Random Signal

Finite vs. Infinite Length

As the name applies, signals can be characterized as to whether they have a finite or infinite length set of values.  Most finite length signals are used when dealing with discrete-time signals or a given sequence of values.  Mathematically speaking, f(t) is a finite-length signal if it is nonzero over a finite interval:

t1 < f(t) < t2

where t1 > -∞ and t2 < ∞. An example can be seen in figure 7. Similarly, an infinite-length signal is defined for all values from -∞ to +∞.

Finite Length Signal
Figure 7. Finite Length Signal

Even vs. Odd

An even signal is any signal f, such that f(t) = f(-t). Even signals can be easily spotted because they are symmetric around the vertical axis. An odd signal on the other hand is a signal f such that f(t) = -f(t).

Even Function
FIgure 8. Even Function
Odd Function
Figure 9. Odd Function


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