# 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).