Signal Classifications

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.

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.

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.

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).

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 +∞.

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).