Q1

Homogeinity of a linear system

A system is a transformation from one signal—called the input—to another signal—called the output or the response of the system. Assume you have a system 𝑓 with time-varying input 𝑥(𝑡), and time-varying response 𝑦(𝑡). Thus:

𝑦(𝑡)=𝑓[𝑥(𝑡)]

If you your system 𝑓 was a linear system, its input-output relationship obeys two important properties: homogeneity and superposition. Which of the following statements express the propertiy of homogeneity mathematically?

Superposition of a linear system

A system is a transformation from one signal—called the input—to another signal—called the output or the response of the system. Assume you have a system 𝑓 with time-varying input 𝑥(𝑡), and time-varying response 𝑦(𝑡). Thus:

𝑦(𝑡)=𝑓[𝑥(𝑡)]

If you your system 𝑓 was a linear system, its input-output relationship obeys two important properties: homogeneity and superposition. Which of the following statements express the propertiy of superposition mathematically?

Eigenfunction of a shift-invariant linear system

Consider the shift-invariant linear system 𝑓 with time-varying input 𝑥(𝑡), and time-varying response 𝑦(𝑡). Thus:

𝑦(𝑡)=𝑓[𝑥(𝑡)]

Sinewaves are the eigenfunctions of a shift-invariant linear system. Which of the following mathematical statements  express this fact correctly?