In Example 10.3.2 we increased the SNR by about 0.3 dB by moving the top-left output point to the origin. What would happen if we moved the output points at the four comers to the positions (±?, 0), (0, ?). As in the example, assume the input has a Laplacian distribution with mean zero and variance one, and ? = 0.7309. You can obtain the answer analytically or through simulation.

Example 10.3.2

Suppose we have to design a uniform quantizer with eight output values for a Laplacian input. Using the information from Table 9.3 in Chapter 9, we would obtain the quantizer shown in Figure 10.4, where A is equal to 0.7309. As the input has a Laplacian distribution, the probability of the source output falling in the different quantization intervals is not the same. For example, the probability that the input will fall in the interval [0, A) is 0.3242, while the probability that a source output will fall in the interval [3A, oo) is 0.0225. Let's look at how this quantizer will quantize two consecutive source outputs. As we did in the previous example, let's plot the first sample along the x-axis and the second sample along the y-axis. We can represent this two-dimensional view of the quantization process as shown in Figure 10.5. Note that, as in the previous example, we have not changed the quantization process; we are simply representing it differently. The first quantizer input, which we have represented in the figure as Xj, is quantized to the same eight possible output values as before. The same is true for the second quantizer input, which we have represented in the