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# Signal Classification

Module by: Melissa Selik, Richard Baraniuk. E-mail the authors

Summary: Describes various classifications of signals.

Note: You are viewing an old version of this document. The latest version is available here.

This module will lay out some of the fundamentals of signal classification. This is basically a list of definitions that are fundamental to the discussion of signals and systems. It should be noted that some discussions like energy signals vs. power signals have been designated their own module for a more complete discussion, and will not be included here.

## "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.

## "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). Analog corresponds to a continuous y-axis, while digital corresponds to a discrete y-axis.

## "Periodic vs. Aperiodic"

Periodic signals repeat with some period T, while aperiodic signals do not.

## "Causal vs. Anticausal vs. Noncausal"

Causal signals are signals that are zero for all negative time, while anitcausal are signals that are zero for all positive time. Noncausal signals are signals that have nonzero values in both positive and negative time.

## "Even vs. Odd"

An even symmetric signal is any signal ff such that ft=ft f t f t . An odd symmetric signal, on the other hand, is a signal ff such that ft=ft f t f t .

Using the definitions of even and odd signals, we can show that any signal can be written as a combination of an even and odd signal. That is, every signal has an odd-even decomposition. To demonstrate this, we have to look no further than a single equation.

ft=1(ft+ft)1(ftf t ) f t 1 2 f t f t 1 2 f t f t
(1)
By multiplying and adding this expression out, it can be shown to be true. Also, it can be shown that ft+ft f t f t fulfills the requirement of an even function, while ftft f t f t fulfills the requirement of an odd function.

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