# classify the system if it's linear , non-linear , time variants or invariants [closed]

classify the system if it's linear , non-linear , time variants or invariants

## closed as too broad by A_A, jojek♦Sep 24 '18 at 20:14

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• What is your current reasoning? How far have you got in answering these questions? – A_A Sep 24 '18 at 7:10
• What's your question? If it is: "solve my homework for me", then this is the wrong place. – Matt L. Sep 24 '18 at 7:24
• I don't really know how to differentiate the graph if it's linear/non-linear or time variants or in-variants . just in case if you can explain me the concept for d and e . i don't really require whole answers . thanks – Kamal Upadhyay Sep 24 '18 at 7:38

Since this is a homework problem I'll just give you few hints that hopefully help you to solve the problem yourself. You should know what linear and time-invariant mean. A system is linear if its response to an input signal $$u(t)=au_1(t)+bu_2(t)$$ equals $$y(t)=ay_1(t)+by_2(t)$$, where $$y_1(t)$$ and $$y_2(t)$$ are the responses to inputs $$u_1(t)$$ and $$u_2(t)$$, respectively. The system is time-invariant if its response to $$u(t-T)$$ equals $$y(t-T)$$, where $$y(t)$$ is the response to $$u(t)$$.
You specifically asked about the systems given in $$d)$$ and $$e)$$. The difference between the two systems is that system $$e)$$ has memory whereas system $$d)$$ is memoryless. The input-output relation of system $$d)$$ is given by $$y(t)=f(u(t))$$, where the function $$f(u)$$ is depicted in the figure. Is the condition for linearity stated above satisfied by this function? Specifically, if the input is $$u(t)=a$$ (referring to the constant $$a$$ in the figure), what is the output for the input signal $$2u(t)$$? Is the output scaled accordingly?
As for time-invariance, does shifting the input signal change the output signal, apart from a shift? If you can answer these questions for $$d)$$, the solution for system $$e)$$ should also be straightforward.