then at time 1, the output decreases back to 0; then, at the next time the output increases back up to 1. Ultimately, we have the output jumping back and forth between 0 and 1 while the input is constant at about 0.5. (You can check this out yourself using either of the shortcuts described in the previous section.) Telecommuni- cations engineers called this phenomena-the output jumping between two values when the input is small-granular noise. The next interesting thing happened at times when the input changed very quickly. Take a look, for example, at the input of Figure 4.33 (b). Here, the output increases by + 8 at each time. (Again, you can check that this is what the output does by using one of the shortcuts I told you about earlier.) But you'll notice from Figure 4.33b that even with the output increasing by + 8 at n each sample time, it still falls further and further behind the input, and it's unable to keep pace with the quickly Figure 4.33 changing input. Telecommunication (a) Granular noise; (b) Overload noise engineers labeled this phenomena overload noise. Chapter Four Figure 4.34 (a) Demonstrating the effect of decreasing S on granular noise (b) Demonstrating the effect of increasing S on overload noise Because granular noise and overload noise were experiences telecommunication engineers wanted to avoid, they found themselves contemplating the following: "We're free to change 8; how can we change 8 to decrease granular noise? And, how can we change 8 to get rid of that unwanted overload noise?" Let's first consider the possibility of changing 8 to decrease the amount of granu- lar noise a DM experiences. Granular noise occurs when the output oscillates above and below a slowly changing input, as in Figure 4.33(a). Let's see what happens if we decrease 8 (Figure 4.34(a)). We see in this case that the amount of oscillating above and below the input has decreased significantly; so, decreasing 8 decreases the granu- lar noise. Let's next consider the case of overload noise, an event which occurs when a