A two-bit quantizer has as input x(nT_s) and as output x̂(nT_s), or

k∆ ≤ x(nT_s) < (k + 1) ∆ → x̂(nT_s) = k∆, k= − 2, − 1, 0, 1

(a) Is this system time-invariant? Explain.

(b) Suppose that the value of ­in the quantizer is 0.25, and the sampled signal is x(nT_s) = nT_s, T_s = 0.1 and −5 ≤ n ≤ 5. Use the sampled signal to determine whether the quantizer is a linear system or not. Explain.

(c) From the results in this problem and the sampling theory, would you say that the A/D converter is a LTI system? Explain.