1.7-12 A system is given by y(t) = { x(t) if x(t) >0 0 if x(t) =< 0 [here =< mea

Question

1.7-12 A system is given by y(t) = { x(t)    if   x(t) >0             0       if  x(t) =< 0      [here =< means equalor less than] (a) Is the system BIBO stable? Justify your answer. (b) Is the system linear? Justify your answer. (c) Is the system memoryless? Justify your answer. (d) Is the system causal? Justify your answer. (e) Is the system time invariant? Justify your answer. Thank you for helping me. 1.7-12 A system is given by y(t) = { x(t)    if   x(t) >0             0       if  x(t) =< 0      [here =< means equalor less than] (a) Is the system BIBO stable? Justify your answer. (b) Is the system linear? Justify your answer. (c) Is the system memoryless? Justify your answer. (d) Is the system causal? Justify your answer. (e) Is the system time invariant? Justify your answer. Thank you for helping me.

Explanation / Answer

b)the sytem is linear ...as it holds the principle ofsuperposition ..i.e it can b added ..y1(t)+y2(t)=x1(t)+x2(t) c)it is a memoryless system as the o/p is function of input atpresent tym ..y(2)=x(2)..o/p doesnt depend on x(1) ie earliero/p d)it is causal as it doesnot anticipate values offuture y(1) gives input of x(1) not x(2) e)no the system is ot tym invariant.. as y(-1)=0 y(-2)=0 y(1)=x(1) y(2)=x(2) so the shift in o/p signal is notidentical to shift in i/p signal a)it is BIBO stable as x(t) is bound a systm is BIBO stablewhen y(t)<B a finite bound value

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