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Solved Problems-1

Problems-1
Check whether the system defined by,
 
Description: Description: Description: 2518.png
 
is time-invariant.
Solution
For input x(t) = x1(t), output Description: Description: Description: 2527.png …(i)
 
For input x(t) = x1(t – T), output, Description: Description: Description: 2533.png …(ii)
 
From the condition of time-invariance, the output should be,
Description: Description: Description: 2539.png…(iii)
 
From equations (ii) and (iii), y2(t) = y1(t – T)
 
Hence, the system is time-invariant.
 




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