Page 28 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 11 SIGNALS AND SYSTEMS

B. Continuous;Time and Discrete-Time Systems:

If the input and output signals x and p are continuous-time signals, then the system is
called a continuous-time system [Fig. I- 15(a)]. If the input and output signals are discrete-time
signals or sequences, then the system is called a discrete-time s?.stem [Fig. I - 15(h)J.

(a) (h)
Fig. 1-15 (a) Continuous-time system; (b) discrete-time system.

C. Systems with Memory and without Memory

A system is said to be memoryless if the output at any time depends on only the input
at that same time. Otherwise, the system is said to have memory. An example of a
memoryless system is a resistor R with the input x(t) taken as the current and the voltage
taken as the output y(t). The input-output relationship (Ohm's law) of a resistor is

An example of a system with memory is a capacitor C with the current as the input x( t )
and the voltage as the output y(0; then

A second example of a system with memory is a discrete-time system whose input and
output sequences are related by

D. Causal and Noncausal Systems:
A system is called causal if its output y(t) at an arbitrary time t = t,, depends on only
the input x(t) for t I to. That is, the output of a causal system at the present time depends
on only the present and/or past values of the input, not on its future values. Thus, in a
causal system, it is not possible to obtain an output before an input is applied to the
system. A system is called noncausal if it is not causal. Examples of noncausal systems are

Note that all memoryless systems are causal, but not vice versa.