Exploring Linear Time-Invariant Systems

What is a Linear Time-Invariant (LTI) system?

• A system that is nonlinear and changes over time.

• A system that is linear and does not change over time.

• A system that is time-variant and has feedback loops.

• A system that only processes discrete signals.

Define the properties of linearity in LTI systems.

• Differentiability and integrability

• Additivity and continuity

• Stability and causality

• The properties of linearity in LTI systems are superposition and homogeneity.

Explain the significance of time invariance in LTI systems.

• Time invariance ensures consistent system behavior regardless of when an input is applied.

• Time invariance allows for different outputs based on input timing.

• Time invariance is only relevant for continuous systems.

• Time invariance means the system can change its behavior over time.

What is the impulse response of an LTI system?

• The impulse response is the output of an LTI system when the input is a Dirac delta function.

• The impulse response is the input to an LTI system when the output is a constant.

• The impulse response is the same as the system's transfer function.

• The impulse response is the average output of the system over time.

How do you determine the output of an LTI system using convolution?

• y(t) = ∫ x(τ)h(t - τ) dτ

• y(t) = x(t) + h(t)

• y(t) = x(t) - h(t)

• y(t) = x(t) * h(t)

What is the relationship between the input and output of an LTI system in the frequency domain?

• The output is the input subtracted from the system's transfer function in the frequency domain.

• The output is the input multiplied by the system's transfer function in the frequency domain.

• The output is the input added to the system's transfer function in the frequency domain.

• The output is the input divided by the system's transfer function in the frequency domain.

Describe the concept of stability in LTI systems.

• Stability in LTI systems means that bounded inputs result in bounded outputs, assessed through BIBO stability and pole locations.

• Stability is determined solely by the frequency response of the system.

• In LTI systems, stability means that all outputs are zero regardless of inputs.

• Stability in LTI systems refers to the ability to amplify inputs indefinitely.

What is the role of the transfer function in analyzing LTI systems?

• The transfer function is used to determine the time domain response of LTI systems.

• The transfer function represents the physical dimensions of the system components.

• The transfer function only applies to nonlinear systems.

• The transfer function characterizes the input-output relationship of LTI systems in the frequency domain.

How can you use the Laplace transform to analyze LTI systems?

• Use the Laplace transform to solve algebraic equations directly without considering LTI systems.

• Apply the Laplace transform only to discrete-time systems for analysis.

• Use the Laplace transform to visualize system behavior without deriving the transfer function.

• Use the Laplace transform to convert differential equations of LTI systems into algebraic equations, derive the transfer function, and analyze system behavior.

What are the differences between causal and non-causal LTI systems?

• Causal LTI systems require more computational resources than non-causal systems.

• Non-causal LTI systems are always unstable.

• Causal LTI systems can only depend on future inputs.

• Causal LTI systems depend on current and past inputs; non-causal LTI systems can depend on future inputs.