Quiz on Linear Time Invariant Systems

What are the two important attributes of a Linear Time Invariant (LTI) system?

• Stability and Linearity

• Causality and Stability

• Linearity and Time-Invariance

• Continuity and Discreteness

What does the impulse response h(t) of a continuous-time LTI system represent?

• The output when the input is a unit step function

• The response of the system to a unit impulse function

• The response of the system to a sinusoidal input

• The output when the input is a constant signal

Which operation is used to find the output of an LTI system given an input signal?

• Differentiation

• Integration

• Summation

• Convolution

What is the formula for the output response y(t) of a continuous-time LTI system?

• y(t) = x(t) - h(t)

• y(t) = x(t) + h(t)

• y(t) = x(t) * h(t)

• y(t) = ∫ x(τ) h(t-τ) dτ

What property of convolution states that the order of the signals does not matter?

In a time-invariant system, if the input signal x(t) produces an output y(t), what will be the output for a time-shifted input x(t+δ)?

What is the convolution integral for continuous-time signals x(t) and h(t)?

• y(t) = ∫ x(τ) h(t-τ) dτ

• y(t) = x(t) * h(t)

• y(t) = ∫ x(t) h(t-τ) dτ

• y(t) = x(t) + h(t)

What is the condition for a continuous-time LTI system to be stable?

• Impulse response h(t) is always positive

• Impulse response h(t) approaches zero as t approaches infinity

• Impulse response h(t) is periodic

• Impulse response h(t) is a constant

What is the discrete-time equivalent of the convolution integral?

In a discrete-time LTI system, what does the impulse response h[n] represent?

• The response to a unit step input

• The response to a unit impulse input

• The response to a sinusoidal input

• The response to a constant input