Welcome to our site!

Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.

  • Welcome to our site! Electro Tech is an online community (with over 170,000 members) who enjoy talking about and building electronic circuits, projects and gadgets. To participate you need to register. Registration is free. Click here to register now.

prove or desprove lenearity..

Status
Not open for further replies.
[latex]

y(t)=e^{-t}x(t)
[/latex]

i need to prove lenearity by constant
and by addition

[latex]

y(t_1)=e^{-t_1}x(t_1)
[/latex]
[latex]

y(t_2)=e^{-t_2}x(t_2)
[/latex]
[latex]

y(t_1)+y(t_2)=e^{-t_1}x(t_1)+e^{-t_2}x(t+2)
[/latex]

[latex]y(t_1+t_2)=e^{-t_1-t_2}x(t_1+t_2)[/latex]

i dont know if [latex]y(t_1+t_2)= y(t_1)+y(t_2)[/latex]
?
 
Last edited:

maxmcp

New Member
[latex]

y(t)=e^{-t}x(t)
[/latex]

i need to prove lenearity by constant
and by addition

[latex]

y(t_1)=e^{-t_1}x(t_1)
[/latex]
[latex]

y(t_2)=e^{-t_2}x(t_2)
[/latex]
[latex]

y(t_1)+y(t_2)=e^{-t_1}x(t_1)+e^{-t_2}x(t+2)
[/latex]

[latex]y(t_1+t_2)=e^{-t_1-t_2}x(t_1+t_2)[/latex]

i dont know if [latex]y(t_1+t_2)= y(t_1)+y(t_2)[/latex]
?

I think you have to multiply the variable t1 or t2 by a constant. so the RHS has eg. 2*t1 in place of t1, and if the result is equal to 2*y then it is linear.

by addition, I am not too sure and wouldnt want to lead you in the wrong direction, but I think you need to prove that [latex]y(t_1+t_2)= y(t_1)+y(t_2)[/latex], which again I would suggest to do by substitution.
 
Status
Not open for further replies.

Latest threads

EE World Online Articles

Loading
Top