ample Xn-1 (and the value a X-n-1) is a very good predicted value for Xn , and SO the error term E is very close to 0. Because of this, a quantizer can be built that is very good and very simple: the quantizer maps the input E (close to 0) to an output with one of only two levels, either +8 or -8 where 8 is a value close to 0. The exact value of 8 depends on the statistics of the input samples Xn. 4.4.5 The Signals in the DM Now we'll see what the different signals in the DM look like, given a particular input to the DM. Have a look at Figure 4.30; this tells you what signals we'll be studying. We will assume that a = 1 to keep this analysis nice and simple. Let's say the input to the DM, point A in Figure 4.30, looks just like Figure 4.31(a). Then, after sampling, the Xn samples that pop out of the sampler (at point B) are shown in Figure 4.31 (b). Quantizer Symbol-to-bit Bit-to-symbol Mapper Mapper B XnP modulator, channel, demodulator Figure 4.30 Block diagram of the DM showing signals of interest We'll study all the other signals of Figure 4.30, starting our study at the first sample time n = 0. We'll assume that the initial value of is 0, i.e., xp=0. Then, following Figure 4.30, we discover the following: (1) At C: the signal = is positive. (2) At D: with a positive value entering the quantizer, the output of the quantizer is +d. (3) At E: once the value É a is sent across the channel, the value at point E is d. (4) At F: the output xo is then Let's consider the next sample time n = 1: (1) At C: we have the signal Let's evaluate the value of xp: xp = a - = Using this xp value, we have = - a. Assuming X1 of Figure 4.31 (b) is larger than a, then the value E1 is positive. (2) At D: the input to the quantizer is positive, SO it follows that the quantizer output É is +d. (3) At E: assuming the value + a is safely sent across the channel, then the value at point E is also +d. (4) At F: finally, the output value is computed as + (value at Chapter Four En x-xnp En , x x-x p x2-28 x3-38 xo O = XO Figure 4.31 Followi