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.

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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?