Chapter 1: Mathematical Representations of Systems

Question 1

Relaxed System Assumption (3)

Answer 1

1. Initial States are unknown.
2. No energy stored
3. Inputs determine outputs.

Question 2

Homogeneity of Set
c1 = scalar
u1 E of Set
N = operation

Answer 2

N(c1, u1) = c1*N(u1)

Question 3

Additivity
u1, u2 E of Set
N = operation

Answer 3

N(u1 + u2) = N(u1) + N(u2)

Question 4

Linear Operator

Answer 4

If superposition is satisfied (homogeneity and additivity) then operation is linear

Question 5

Time Invariance vs Time Varying

u(t) -> N -> y(t)

Answer 5

time invariance: u(t+T) -> N -> y(t+T)

time varying: u(t+T) -> N -> y(t)

Question 6

Causality vs Non-Causality

Answer 6

Casuality: depends on past/current values of input

Non-Causality: depends on future values of input (physically impossible)

Question 7

Instantaneous vs Dynamic

Answer 7

Instantaneous: depends on present
Dynamic: depends on past or future values