es that come out of the sampler, SO this number is always equal to the sampling rate. Chapter Four Finally, there's the bit rate. This indicates how many bits per second come out of the symbol-to-bit mapper. This number can be evaluated by the simple computation bit rate = symbol rate bits/symbol (4.52) 4.3.3 The "Good" PCM Telecommunication engineers needed a way to evaluate how well a source coder, like the pulse code modulator, was working. Ultimately, they decided that a "good" source coder was one that had two things going for it. First, the amount of error in the quan- tizer part should be small; that is, they wanted a large SQNR. They called this "good" because it meant only a very little bit of information was being lost at the quantizer part. Second, the bit rate of the source coder should be small. These engineers called small bit rates "good" because they discovered that a smaller bit rate means a smaller bandwidth for the source coder output signal (shown in Figure 4.24), and that was good because a lot of communication channels would only transmit signals with a small bandwidth. High bit rate = many bits/sec Low bit rate = few bits/sec T1 (small) T2 (big) in frequency domain in frequency domain -1/T1 1/T1 (big) -1/T2 1/T2 (small) BW~2/T1 BW~2/T1 Figure 4.24 Illustrating that high bit rate leads to large signal bandwidth Source Coding and Decoding: Making it Digital However, one bright engineer saw a problem. "Wait a minute! You telecommuni- cation guys want opposite things. Your number-one want (large SQNR) and your number-two want (small bit rate) are opposites. Let's say you want a quantizer with a high SQNR (low error). Then you'll need a quantizer with a lot of allowed output levels, for example, 1024. But this means you've got to have 10 bits (210 = 1024) for each symbol, which will mean a HIGH bit rate (as we see from equation (4.52))." He was right. Since what we want are opposite things, we have to define a "good" source coder like this: 1. If the SQNR is fixed, we get a very small bit rate (