CLASSIFICATION OF SYSTEMSCLASSIFICATION OF SYSTEMS

PROF.SATHEESH MONIKANDAN BHOD-ECE

INDIAN NAVAL ACADEMY, EZHIMALA

sathy24@gmail.com

92 INAC-L, AT-15

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 signalSystem

Basic operations on signalsBasic operations on signals

Basic Operations on SignalBasic Operations on Signal

System PropertiesSystem Properties

Stable and Unstable SystemsStability 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.

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.)

Memoryless systemsThe 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 .

t0t0

v o( t 0 ) v i( t0 )v o( t ) t≠t0

v 0( t )=R2

R1+R2

v i( t )

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 )=Cdv ( t )dt

v ( t )=1C∫−∞

ti (τ )dτ

——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 )=∫−∞

tx (τ )dτ

Systems with memory

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 ≤ toThen y1(t) = y2(t) for all t ≤ to

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

Time-Invariant Systems

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

LINEAR AND NONLINEAR SYSTEMSMany systems are nonlinear.

System behavior is very unpredictable because it is highly nonlinear.

Linear systems can be analyzed accurately.

Invertibility

x(t) x(t)y(t)H 1−H

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

Invertibility and Inverse Systems

Systemx [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 )=

12y ( 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

Series(cascade) Interconnection

Parallel, Interconnection

Interconnection of systemsInterconnection of systems

System 1 System 2

System 1

System 2

+Input Output

Input Output

Interconnection of systemsInterconnection of systems

•Feedback Interconnection

System 1

System 2

Input Output