# Time Invariance

Discussion in 'Homework Help' started by NguyenDon, Feb 15, 2014.

1. ### NguyenDon Thread Starter New Member

Feb 15, 2014
9
1
I have a system given,

y(t) = ay(t-1) + x(t)- 2x(t-2).

As I understand a system is time invariant if

x(t) -> y(t)

and

x(t-T) -> y(t-T).

What is confusing me is the delayed output that this system depends on. Is this a time invariant system? Thanks.

2. ### NguyenDon Thread Starter New Member

Feb 15, 2014
9
1
I figured splitting the equation into two time intervals, t > 1 and t < 1.

At t < 1, I ignored the delayed output ay(t-1) in the system and solved for y(t) in terms of x only. I then delayed both input and output signals and found equivalence.

Then for t > 1, I added ay(t-1) back into the input. I replaced y(t-1) with what I found earlier with all time parameters delayed by 1. I was then able to find equivalence again from delaying the inputs and the outputs which confirmed TI.

Can anyone confirm that this is correct?

3. ### WBahn Moderator

Mar 31, 2012
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