king it Digital xs(t) xs(t) Symbol-to-bit Quantizer mapper Sampler Figure 4.23 PCM and how it works Finally, a device called a symbol-to-bit mapper takes in the quantized samples (t) and, for each sample in s(t) that comes in, it outputs a set of bits, O's and 1's. A 0 may be represented by a short pulse of -5V and a 1 by a short pulse of +5V. Let me explain how this device works by example. Let's say the quantizer outputs samples which take on one of four levels-for example, the output samples of the quantizer are values in the set {0,1,2,3}. The symbol-to-bit mapper associates a unique set of bits with each sample; for example, it associates the bits 00 with the symbol 0, it associates the bits 01 with symbol 1, and it links the bits 11 with symbol 3. When a given sample comes in, it puts out the bits it has associated with that sample. It's really quite a simple device, and you can look at Figure 4.23 to get a better feel for how it works. To sum up, the tag-team combination of sampler, quantizer, and symbol-to-bit mapper together take an analog signal (t) and map it to a digital signal, in this case a set of bits. 4.3.2 PCM Talk Telecommunication engineers associate a number of terms with the pulse code modu- lator of Figure 4.23, as a way to help describe its operation. I'll discuss three of these key words here. First, there's sampling rate, or how many samples per second the sampler creates. As you'll probably recall, the sampling rate is usually chosen to be at least two times the maximum frequency of the input, because if you do this, then all the information in the original signal is kept in the samples. Next, there's the term symbol rate. This is the number of samples per second that leave the quantizer. Since the quantizer creates one sample out for each sample that comes in, the symbol rate is also the rate of the symbols that come into the quantizer. But, if you take a quick peek at Figure 4.23, you'll notice that the number of samples that come into the quantizer exactly matches the number of sampl