Digital Signal Processing Reference
In-Depth Information
x
(
t
),
Input
Signal
y
(
t
),
Output
Signal
System, T
y
(
t
) = T [
x
(
t
) ]
Fig. 1.6
Signal processing system as an operator
1.1.8 Classification of Systems
A system can belong to one or more of the following categories.
1. Analog, discrete-time, and digital (discrete-time quantized) systems. Analog
systems operate on continuous-time signals, discrete-time systems operate on
discrete-time signals and digital signals operate on discrete-time quantized
signals.
2. Time-varying (non-stationary) and time-invariant (stationary) systems:ina
time-invariant system, shifts in the input produce corresponding shifts in the
output. That is, if a system input x(t), gives an output y(t), then an input of
x(t - t
o
) will give an output of y(t - t
o
). This can be expressed more formally
as:
If
y
ð
t
Þ¼T½
x
ð
t
Þ
then
y
ð
t
t
o
Þ¼T½
x
ð
t
t
o
Þ
where t
o
is a constant positive time-shift.
3. Causal and non-causal systems: the output of a causal system at time, t,is
only dependent on values of the input up to and including time t. The output is
not dependent on input values beyond t. Practically realizable systems must be
causal— otherwise they would need to be able to predict the future to generate
outputs.
4. Static (memoryless) and dynamic (with memory) systems: a system whose
output does not depend on either a previous or future value of the input signal
x(t) is called memoryless, i.e., y(t) is a function only of x(t). In a dynamic
system the output depends on inputs at either past or future values of time. An
inductor which has voltage as input and current as output is an example of a
system which is dynamic. The voltage across the inductor is v(t) = L
di/dt and
the current is i
L
¼ð
1
=
L
Þ
R
t
1
v
L
ð
t
Þ
dt. Hence the inductor has a memory. The
same argument is applicable to a capacitor, which has current as input and
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