An A/D converter can be thought of composed of three subsystems: a sampler, a quantizer, and a coder.

(a) The sampler, as a system, has as input an analog signal x(t) and as output a discrete-time signal x(nT_s) = x(t)|_t=nTs, where T_s is the sampling period. Determine whether the sampler is a linear system or not.

(b) Sample x(t) = cos (0.5πt) u(t) and x(t − 0.5) using T_s = 1 to get y(nT_s) and z(nT_s), respectively. Plot x(t), x(t − 0.5) and y(nT_s) and z(nT_s). Is z(nT_s) a shifted versions of y(nT_s) so that you can say the sampler is time-invariant? Explain.