Let x(t) = cos(? t)[u(t) ? u(t ? 2)] be the input of a zero-order hold sampler. The sampler samples every T_s sec starting at t = 0, and the impulse response of the zero-order hold is h(t) = u(t) ? u(t ? T_s). The quantizer and coder shown in Figure 8.12 in the text is used to generate a digital signal.

(a) Let T_s = 0.5 sec/sample, find the values of the sampled signal using the ideal sampler. Determine the corresponding digital signal.

(b) Suppose now that we let T_s = 0.25 sec/sample. Carefully plot the sampled signal using the ideal sampler and then plot the output y(t) of the zero-order hold system. Determine the corresponding digital signal.

(c) For the above two cases find and plot the quantization error ?(nT_s) = x(nT_s) ?x?(nT_s), where x?(nT_s) is the output of the quantizer.

Figure 8.12:

f(nT,) 01 – 2A - A 00 x(nT,) A 24 11 A 10 2A