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up vote 3 down vote favorite 1 $T(x[n]) = ax[n] + b$ $ T(alpha_{1}x_{1}[n] + alpha_{2}x_{2}[n]) = alpha_{1}ax_{1}[n]+ alpha_{2}ax_{2} [n] +b $ $ alpha_{1}T(x_{1}[n] ) + alpha_{2}T(x_{2}[n]) = alpha_{1}(ax[n]+b) + alpha_{2}(ax_{2} [n] +b) $ therefore they are not equal so the system is non-linear? or would it be something like this: $ T(alpha_{1}x_{1}[n] + alpha_{2}x_{2}[n]) = alpha_{1}ax_{1}[n]+alpha_{1}b + alpha_{2}ax_{2} [n] + alpha_{2}b $ $ alpha_{1}T(x_{1}[n] ) + alpha_{2}T(x_{2}[n]) = alpha_{1}(ax[n]+b) + alpha_{2}(ax_{2} [n] +b) $ and therefore they are equal so the system is linear? homework system-identification share | improve this question edit