Let ‰¤ t ‰¤ 1 ‰¤ t ‰¤ 1, and zero otherwise, be the input to a 2 bit analog-to-digital converter.

(a) For a sampling period T_s = 0.025 sec. determine and plot using MATLAB the sampled signal

(b) The 4-level quantizer (see Figure 1.2) corresponding to the 2-bit A/D is defined as

kˆ† ‰¤ x(nT_s) < (k + 1) ˆ† †’ xÌ‚(nT_s) = kˆ†, k = ˆ’2, ˆ’1, 0, 1

where x(nT_s), found above, is the input and xÌ‚(nT_s) is the output of the quantizer. Let the quantization step be ˆ† ­= 0.5. Plot the input/output characterization of the quantizer, and find the quantized output for each of the sample values of the sampled signal x(nT_s).

(c) To transform the quantized values into unique binary 2-bit values, consider the following code

xÌ‚(nT_s) = €“2ˆ† †’ 10

xÌ‚(nT_s) = €“ˆ† †’ 11

xÌ‚(nT_s) = 0ˆ† †’ 00

xÌ‚(nT_s) = ˆ† †’ 01

Obtain the digital signal corresponding to x(t).

|x(nT,) = x(t)|t=nTs