Shift-Invariant System Example- Consider the up-sampler with an input-output relation given by x uin x{n/L],n=0,±L,±2L otherwise For an input xin]=xin-noi the output xluln Is given by ∫x1[n/L,n=0,±L,±2,… otherwise ∫x(m-Lm)/L,n=0,±L,±2L 0 otherwise Copyright C 2001, S K. MitraCopyright © 2001, S. K. Mitra 17 Shift-Invariant System • Example - Consider the up-sampler with an input-output relation given by • For an input the output is given by    =   = , otherwise [ / ], , , ,..... [ ] 0 x n L n 0 L 2L xu n [ ] [ ] n no x1 n = x − [ ] x1,u n    =   = , otherwise [ / ], , , ,..... [ ] , 0 1 0 2 1 x n L n L L x u n    − =   = , otherwise [( )/ ], , , ,..... 0 x n Lno L n 0 L 2L