iagram, the value is created at the DM and decoder. We'll start at the source decoder, because it's easier. At the source decoder, the value X is available at the output. So, all we do- and the dashed lines of Figure 4.29 show this-is take the available X delay it by one sample time (with the z-1 block) and multiply it by a; and then we've got it: = At the source coder, the value of x is not readily available, SO what the dashed lines on the coder side of Figure 4.29 do is this: (1) first make X by adding x, and É (this is how x is made at the decoder), then (2) delay the x that's just made and multiply it by a to get =a X,-- The Sampler and the Quantizer in the DM While the block diagram of the DM is well-described by Figure 4.29, and a description of how it works is also given, there are a few things about the DM that have been left unsaid, and in this section I want to say them. These are things regarding the sampler and the quantizer. The Sampler: First, we said earlier that the idea behind the DM was that if you sampled a signal fast enough, then the previous sample Xn-1 was a good predicted value for X , and we modified that slightly and came up with the predicted value of n-1' where a is a value close to 1. What I want to explore here is: how fast does the sampler in a DM actually sample the signal X (t) such that the sample Xn-1 is a very good predicted value of X ? I don't know exactly how telecommunication engineers came up with this, and I expect that it was trial and error, but ultimately when x(t) is a speech signal the sampler tends to work at four times the Nyquist rate, or eight times Source Coding and Decoding: Making it Digital the Nyquist rate; that is, the sampler tends to work at eight times or sixteen times the maximum frequency of the incoming signal X (t). The Quantizer: Next, let's consider the quantizer. The quantizer maps the predicted error, E to an output É with one of N levels. How many output levels (N) does the quantizer use? The sampling rate in a DM is SO high that the previous s