Figure 4.12. Here, we see a quantizer with input X's (t) (the output of a sampler). Let's assume that the quantizer allows output amplitudes from the set {0, 1, 2, 9}. Consider the sample labeled A on the figure, with an amplitude of 3.3322. It enters into the quantizer. The quantizer changes the amplitude to the closest allowed amplitude, which in the case of sample A is 3. So we end up with sample A The quantizer changes sample B in the same way. OK, now that you've got it, I'm going to give you a more technical description, first in words, then using math, and finally using a picture. Don't let any of this intimi- date you, because you've already got it! In words, a quantizer is a device that maps the amplitude of the incoming signal to the nearest allowed level. Mathematically, a quantizer is a device that performs the mapping x = Q(x), where x refers to the quantizer input, x describes the quantizer output, and Q0.) is a function which maps the values (-00,00) to the closest value in the set C = {y1, Y2,.. yn}, i.e., Q: (-00,00) -> C. Graphically, given an input of x, the quantizer output x can be evaluated using a graph of the form shown in Figure 4.13. This figure y2=-1 shows that the output corresponds to the allowed amplitude closest to the amplitude of the input. 1 = -2 Figure 4.13 Figure illustrating how a quantizer can be described graphically Source Coding and Decoding: Making it Digital Example 4.3 Consider the quantizer with the input shown in Figure E4.3(a) and with an input amplitude-output amplitude relationship drawn in Figure 4.3(b). Draw a plot of its output. x (output amplitude) X (input amplitude) Figure E4.3 (a) Quantizer input (b) input amplitude-output amplitude relationship describing quantizer Solution: When the input between time 0 and 1 is of amplitude 1.3, then (using Figure E4.3(b)) its output between those times is amplitude 1. You can see that in Figure E4.4. With the input between times 1 and 2 set to 3.1, then the output between those times is set at 3. Finally, with input betw