urrent sample Xn is simply the previous sample value Xn-1 That is, a good predicted value of the sample Xn is However, as one telecommunication engineer was quick to point out, there was a problem with this idea. "If you use she argued, "there's no way to add back x," at the decoder (Figure 4.28), because Xn-1 is a sample of the input signal, and the decoder (in the receiver end of the channel) has no way to create exactly that." And with that the telecommunication engineers scratched their collective heads for a while, until one day one of them screamed, "I've got it! Have a look at this." She pointed to the source decoder in Figure 4.28. "While the source decoder doesn't have access to the Xn (or Xn-1), it does have access to X (and So, we can use -1 as the predicted value, rather than Xn-1." That seemed a good idea, and everyone was in agreement. After some time and a bit of hard work, engineers decided to use X as the predicted value, that is, Some engineers decided to fine tune this idea, and as they played around with it, they found that a slightly better choice of xp is where a is a value very close to, but just a little less than, 1; specifically, they figured out that the optimal value of a was (4.53) where In what follows, we'll use the predicted value x,==a Chapter Four received Symbol-to-bit Bit-to-symbol Quantizer sampler Mapper Mapper modulator, channel, demodulator xnp = ax n-1 Xmp = ax Source decoder Delta modulator (DM) for DM Figure 4.29 The delta modulator and source decoder block diagram The Block Diagram of the DM Let's now take a look at the block diagram of the DM to get an understanding of how this device is built. Both the DM and the source decoder are shown in the block diagram of Figure 4.29. The solid line shows that this DM and source decoder has the same form as the general predictive coder and source decoder of Figures 4.27 and 4.28. The dashed lines show the creation of the predictive value xx=ax, at the DM and decoder. Let's take some time out now and describe how, in this block d