BASIC PROPERTIES OF SYSTEMS

1. CLASSIFICATION OF SYSTEMSCLASSIFICATION OF SYSTEMS
PROF.SATHEESH MONIKANDAN B
HOD-ECE
INDIAN NAVAL ACADEMY, EZHIMALA
sathy24@gmail.com
92 INAC-L, AT-15

2. Fundamentals of Signals and SystemsFundamentals of Signals and Systems
 System: an entity or operator that manipulates
one or more signals to accomplish a function,
thereby yielding new signals.
Input signal Output signal
System

3. Basic operations on signalsBasic operations on signals
Basic Operations on SignalBasic Operations on Signal

4. System PropertiesSystem Properties

5. Stable and Unstable Systems
Stability can be defined in a variety of ways.
–Definition 1: a stable
system is one for which
an incremental input
leads to an incremental
output.
–Definition 2:A system
is BIBO stable if every
bounded input leads to
a bounded output.

6. 2.Memory /Memoryless
• Memory system: present output value depend on
future/past input.
• Memoryless system: present output value
depend only on present input.
• Example
System Properties(cont.)System Properties(cont.)

7. Memoryless systems
The output of a memoryless system at some time
depends only on its input at the same time .
For example, for the resistive divider network,
Therefore, depends upon the value of
and not on .
t0
t0
vo(t0) vi(t0)
vo(t) t≠t0
v0(t)=
R2
R1+ R2
vi(t)

8. Systems with Memory
Note that v(t) depends not just on i(t) at
one point in time t .Therefore, the system
that relates v to i exhibits memory.
i(t)=C
dv(t)
dt
v(t )=
1
C
∫−∞
t
i(τ )dτ

9. ——memoryless
——memoryless
y [n]={2x [n]−x2
[n]}
2
①
y (t)=x (t)②
③ summer y [n]= ∑
k =−∞
n
x[k ]
④ delay y [n]=x[n−1]
⑤ integrate y(t)=∫−∞
t
x(τ)dτ
Systems with memory

10. Causal and Non-causal Systems
Mathematically (in CT):
A system x(t) → y(t) is causal
if x1(t) → y1(t) and x2(t) → y2(t)
and if x1(t) = x2(t) for all t ≤ to
Then y1(t) = y2(t) for all t ≤ to

11. System Properties(cont.)System Properties(cont.)

12. Time-Invariant Systems

13. System Properties(cont.)System Properties(cont.)

14. LINEAR AND NONLINEAR SYSTEMS
Many systems are nonlinear.
System behavior is very unpredictable
because it is highly nonlinear.
Linear systems can be analyzed accurately.

15. Invertibility
x(t)
x(t)y(t)
H 1−H
System Properties(cont.)System Properties(cont.)

16. Invertibility and Inverse Systems
System
x[n]
x(t) y(t)
y[n] Inverse System
w [n]=x[n]
w (t)=x(t)
x(t)
y(t)=2x (t)
y(t) w (t)=x(t)
w (t)=
1
2
y(t)
y [n]= ∑
k =−∞
n
x[k ]
x[n] y[n]
w [n]=y[n]−y[n−1]
w [n]=x[n]
——noninvertible systems
不可逆系统

17. Series(cascade) Interconnection
Parallel, Interconnection
Interconnection of systemsInterconnection of systems
System 1 System 2
System 1
System 2
+
Input Output
Input
Output

18. Interconnection of systemsInterconnection of systems
•Feedback Interconnection
System
1
System
2
Input Output