**Practice Question on "Signals and Systems"**

Topic: System Properties

## Question

The input x(t) and the output y(t) of a system are related by the equation

$ y(t)= t^2 x(t) $

Is the system memoryless? Justify your answer.

You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!

### Answer 1

Yes. Since the requirement for a system to be memoryless is that for any time $ t_0 \in \Re $, $ y(t_0) $ depends only on the input $ x(t_0) $.

In other words, since this system is dependent only on current values of t, not future or past values, we say it is a memoryless system. --Darichar 14:41, 5 February 2011 (UTC)

- Instructor's comment: Yes, the above definition (first part of the answer) is correct answer. Slight correction for the second part:

"In other words, since this system's output is dependent only on the current value of the input, not future or past values, we say it is a memoryless system." -pm,

Question: Is there a proper way to prove this mathematically? or do we just simply answer in words based on intuition?

### Answer 2

Write it here.

### Answer 3

Write it here.