## 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.

# 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

*. An example can be seen in figure 7. Similarly, an infinite-length signal is defined for all values from*

**t2 < ∞**

**-∞ 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)**You can download this page for free at http://cnx.org/contents/97e7bfc1-2a8c-4b4a-ad8b-6a94370086c3@24