Properties of Systems Memoryless, Causal, time invariant, linearby itsdinamo Tags: signals and systems 

#1
Aug2011, 07:43 PM

P: 1

Hi, I need a hand with my reasoning on the following question.
I have answered all the questions, but not too sure weather they are correct. Please guide me or point me on the right direction if they are not correct. Regards 1. A system defined by the following equation y(t)=[x(t2)]^2 Is the system Memoryless, Causal, Time Invariant, linear The attempt at a solution Memoryless ? y(t)=x(t2) has memory, the output is equal to the input two seconds ago. y(t)=[x(t)]^2 = memoryless, the output at time t0 depends only on the input value at time t0. Now, y(t)=[x(t2)]^2 can be thought as y(t)=[x(t2)*x(t2)] right?, if so, my best guess would be that the system y(t)=[x(t2)]^2 has memory. Causal? by definition; A system is causal if the output at any time t0 is dependent on the input only for t<=t0. y(t)=[x(t2)]^2 = causal Time Invariant? by definition if x(t)>y(t), then x(tt0)>y(tt0) so; x(tt0)>[x((tt0)2)]^2 y(tt0)=[x((tt0)2)]^2, Therefore, y(t)=[x(t2)]^2 is time invariant. linear ? A system is linear if it is homogeneous and additive. Homogeneous Property if x(t)>y(t), then ax(t)>ay(t) a= alpha Additive Property if x1(t)>y1(t), and x2(t)>y2(t), then x1(t)+x2(t)>y1(t)+y2(t), x(t)>y(t)=[x(t2)]^2 multiply input by alpha a, then ax(t)>[ax(t2)]^2 ay(t)>a[(x(t2))^2] system y(t)=[x(t2)]^2 is not homogeneous, thus not linear. 


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