System Classification

Question 1

System

Answer 1

Any connection of components or devices with at least one input signal and at least one output signal

Question 2

System examples

Answer 2

Computer; all the circuits in ENGR 221, ELEN 223, ELEN 224, ELEN 335; electromechanical device; automotive vehicle; chemical power plant

Question 3

System Classification

Answer 3

1. Memoryless vs. Dynamic
2. Causal vs. Non-causal
3. Stable vs. Unstable
4. Linear vs. Non-linear
5. Time invariant vs. Time variant

Question 4

Memorlessness

Answer 4

If a system depends only on the current input to produce an output, the system is called memoryless

Y(t) does not require past of future values of x(t)

Question 5

Dynamic

Answer 5

System depends on the past input values

Input and output at different times

Question 6

Causality Property of Systems

Answer 6

A system is called causal if the output at any time depends only on the past and/or present values of the input. In other words, the output doesn’t depend on the future input values

Question 7

Non-Causal

Answer 7

If the output depends on future input values

Question 8

Stability Property of Systems

Answer 8

A system is called stable if the output values are finite for finite input values

A system is called unstable if it can generate an output signal with an infinite value for a finite input signal

Question 9

Criterion to determine whether a system is stable or not

Answer 9

Bounded input bounded output (BIBO) criterion

Question 10

Bounded input bounded output (BIBO) criterion

Answer 10

If an input signal is bounded by a finite positive number Bx, then if there exists a finite positive number By that bounds the output signal, the system is called stable.

Question 11

Time-Invariance Property of Systems

Answer 11

If y(t) is the output when the input is x(t), and y(t-c) is the output when the input is x(t-c), then the system is called time invariant.

Question 12

Linearity Properties of Systems

Answer 12

A system is called linear if it satisfies the linearity property (additivity property, scaling or homogeneity property)

Question 13

Additivity Property

Answer 13

Suppose that the outputs of a system are y1(t) and y2(t) when the input are x1(t) and x2(t). Then, if the output is y1(t)+y2(t) when the input is x1(t)+x2(t), the system satisfies the additivity property.

Question 14

Scaling Property

Answer 14

Suppose y(t) is the output when the input is x(t). Then if the output is cy(t) when the input is cx(t), the system satisfies the scaling property.