Practice Question on "Signals and Systems"

More Practice Problems

Topic: System Properties


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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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.

Back to ECE301 Spring 2011 Prof. Boutin

Alumni Liaison

Ph.D. 2007, working on developing cool imaging technologies for digital cameras, camera phones, and video surveillance cameras.

Buyue Zhang