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Signals and Systems

Q1: Which one of the following is the correct statement of the system characterized by the equation y(t) = ax(t) + b?

A linear for any value of b

B linear if b > 0

C linear if b < 0

D non-linear

ANS:D - non-linear

Let y1(t)=ax1(t)+b & y2(t)=ax2(t)+b.

Let x3(t)=x1(t)+x2(t), then,

y3(t)=ax3(t)+b=a[x1(t)+x2(t)]+b=ax1(t)+ax2(t)+b => y1(t)+y2(t).

Hence nonlinear, because linearity property does not hold.



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