Determine whether the system is linear?
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...