2.3 Definition and Classification of Signals

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27

time t/s

time t/s

Fig. 2.16: Rectangular pulse in the form of an acausal signal sa(t) (left) and a causal signal sk(t)

(right).

2.3.4 Causal and Acausal Signals

Causality as a property is often used in the classification of signals and systems to

describe switch on/off processes. Figure 2.16 shows a causal signal (left), where the

switch-on process is in the past, and a causal signal (right), which was only switched

on at positive time.

Mathematically, a signal s(t) is called causal if it does not exist or is identical to 0

for all times t < 0. If this condition is not fulfilled, an acausal signal is present, thus:

s(t)causal =

{

{

{

s(t)

t ≥0

0

t < 0

,

s(t)acausal =

{

{

{

s(t)

t ≥0

s(t)

̸= 0

t < 0

,

∀t .

(2.30)

The classification causal/acausal also finds its application in the description of sys-

tems. In contrast to signals, the causal connection, i.e. that an effect (output values of

a system) cannot emerge before the cause (input values of a system), is only fulfilled

for systems whose output values are equal to zero for times t < 0. Systems that do

not fulfil this condition are called acausal and also have no real physical cause-effect

relation.

2.3.5 Energy and Power Signals

The concepts of energy and power are fundamental quantities in physics that can be

used, for example, to determine the electrical energy required for the displacement

of an electron in the electrical field of a capacitor. The assignment of these quantit-

ies to a purely analytical signal, on the other hand, is not obvious, since mathemat-

ical functions have no physical dimension. In section 2.1 the process of information

transfer through the energisation or materialisation of information into information

signals is clarified. Signals are thus the energetic or materialised form of information,