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Signal Classification

Module by: Melissa Selik. E-mail the author

Summary: Describes various classifications of signals.

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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.

Figure 1
Figure 1 (sigclass1.jpg)

"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.

Figure 2
Figure 2 (sigclass2.jpg)

"Periodic vs. Aperiodic"

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

Figure 3
(a) A periodic signal with period T0 T 0
Figure 3(a) (sigclass3.jpg)
(b) An aperiodic signal
Figure 3(b) (sigclass4.jpg)

"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.

Figure 4
(a) A causal signal (b) An anticausal signal (c) A noncausal signal
Figure 4(a) (sigclass5.jpg) Figure 4(b) (sigclass6.jpg) Figure 4(c) (sigclass7.jpg)

"Even vs. Odd"

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

Figure 5
(a) An even signal (b) An odd signal
Figure 5(a) (sigclass8.jpg) Figure 5(b) (sigclass9.jpg)

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.

f⁢t=1⁢(f⁢t+f⁢−t)−1⁢(f⁢t−f⁢− 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 f⁢t+f⁢−t f t f t fulfills the requirement of an even function, while f⁢t−f⁢−t f t f t fulfills the requirement of an odd function.

Example 1

Figure 6
(a) The signal we will decompose using odd-even decomposition
Figure 6(a) (sigclass10.jpg)
(b) Even part: e⁢t=(1−2)⁢(f⁢t+f⁢−t) e t 1 2 f t f t
Figure 6(b) (sigclass11.jpg)
(c) Odd part: o⁢t=(1−2)⁢(f⁢t−f⁢−t) o t 1 2 f t f t
Figure 6(c) (sigclass12.jpg)
(d) Check: e⁢t+o⁢t=f⁢t e t o t f t
Figure 6(d) (sigclass13.jpg)

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