Linear Discrete-Time Systems Definition-If yln]is the output due to an aput x,[n] and y2n] is the output due to an input x2[n then for an input xn=axIn Bxoln the output is given by yn]=ayin]+By2ln above property must hold for any arbitrary constants a and B, and for all possible inputs x[n]and xiN] Copyright C 2001, S K. MitraCopyright © 2001, S. K. Mitra 10 Linear Discrete-Time Systems • Definition - If is the output due to an input and is the output due to an input then for an input the output is given by • Above property must hold for any arbitrary constants and and for all possible inputs and [ ] y1 n [ ] x1 n [ ] x2 n [ ] 2 y n [ ] [ ] [ ] x n = x1 n +  x2 n [ ] [ ] [ ] y n = y1 n +  y2 n   , [ ] x1 n [ ] x2 n