System Characteristics

Question 1

If for a system x(t) → y(t) and z(t) → f(t), which shows linearity?
► ax(t) + bz(t) → ay(t) + bf(t)
► ax(t) - bz(t) → ay(t) + bf(t)
► ax(t) + bz(t) → by(t) + af(t)

(Assume a,b are scalar constants)

Answer 1

ax(t) + bz(t) → ay(t) + bf(t)

Question 2

If for a system y(t) → x(t) and z(t) → g(t), which shows time invariance?

► y(t-τ) → g(t-τ)
► y(t-τ) → x(t-τ)
► z(t+τ) → g(t-τ)

(Assume τ is a scalar constant)

Answer 2

y(t-τ) → x(t-τ)

Question 3

We can describe many continuous time systems using linear constant coefficient differential equations. What is the equivalent form for DISCRETE time systems?

Answer 3

linear constant coefficient difference equations

Question 4

What is the general linear constant coefficient differential equation form (mathematically)?

Answer 4

Question 5

What is the general linear constant coefficient difference equation form (mathematically)?

Answer 5

Question 6

Given: cos(2t) → [LTI system] → y(t)
If we know that for the LTI system the frequency response H(jw) satisfies:
|H(2j)| = 4, ∠H(2j) = π/4, then what is y(t)?

Answer 6

4cos(2t+π/4)

Question 7

When is a system considered causal?

Answer 7

The current output depends only on current and past inputs (not future)

Question 8

What is the homogeneity condition for linearity?

Answer 8

Scaling the input scales the output:
If x(t) → y(t) then αx(t) → αy(t)

α is a scalar constant

Question 9

What is the additivity condition for linearity?

Answer 9

Adding inputs results in an output which is the addition of the individual outputs:
If x₁ → y₁ and x₂ → y₂,
then x₁+x₂ → y₁+y₂

Question 10

What is the time invariance condition?

Answer 10

A shift in time of the input results in the same time shift in the output
If x(t) → y(t) then x(t-τ) → y(t-τ)

τ is a scalar constant

Question 11

What does LTI stand for?

Answer 11

Linear, Time-Invariant

Question 12

An LTI System is memoryless if and only if the output depends only on _______.

Answer 12

present input

This means that the output does not rely on past or future inputs.

Question 13

A causal system is defined as one where the current output depends on _______.

Answer 13

current and past inputs only

This means that future inputs do not affect the current output.

Question 14

The concept of stability in an LTI system refers to the condition where a bounded input leads to a _______.

Answer 14

bounded output

This is a key requirement for the stability of LTI systems.

Question 15

In the context of LTI systems, what does BIBO stand for?

Answer 15

Bounded Input, Bounded Output

This concept is crucial for determining the stability of the system.