een times 2 and 3 set to 3.9, then the output from Figure 4.3(b) becomes 3. The final output plot is found in Figure E4.4. Figure E4.4 Quantizer output Who wants it? Now that you know what a quantizer is, you may be scratching your head wondering who the heck would want to use a device that maps an incoming amplitude to an output amplitude that must be one of N allowed values? The answer is: almost every telecommunication engineer who wants to build a digital telecommunication system/ network. And the reason is best explained by example, as follows. Let's say you are acting as a quantizer: I shout out a number between 1 and 10, and you shout back the closest integer between 1 and 10. So I shout "1.4" and you shout back "1". I scream "5.93" and you say "6". Let's say we decide we want to build a Chapter Four digital communication system. The information I shouted, any number between 1 and 10 (6.984, for example) cannot be represented by a digital signal (because there are an infinite quantity of numbers between 1 and 10). On the other hand, the numbers you shouted back-1, 2, 3, 10-can be represented by a digital signal (because there are only 10 possible numbers)-so this information can be sent using a digital commu- nication system. So, the quantizer performs a very important task. It turns an incoming signal into a digital signal, which can be communicated using a digital communication system. Of course, some of the amplitude information is lost when we quantize a signal. When I said 1.4 and you replied 1, we "lost" the .4. As you'll see later, we try to build quantiz- ers in such a way as to minimize the loss of information. Quantizer Terms Telecommunication engineers, with the best of intentions, have created several terms and definitions to make it easier to describe a quantizer. First, there's the word codebook, C. A quantizer changes the amplitude of the input to one of N allowed output amplitudes. The set of N allowed output amplitudes is collectively called the codebook, or C for short. Because C contains