 amplitude comes into the quantizer; that is, we assume we know the probability density function of the amplitudes coming into the quantizer, px(x), where X is the incoming amplitude. Assuming we know px(x), , the first overall measure of quantizer performance is mean squared error, or mse for short. Mean squared error, as the name suggests, is just the average (or mean) of the error e(x) squared; that is, mean squared error is mse = (4.18) Since we want a quantizer to have a small error (difference between input ampli- tude and output amplitude), it makes sense that engineers call a quantizer with a small mean squared error a "good one." The second overall measure of quantizer performance is signal to quantization noise ratio, or SQNR for short. (Some other telecommunication books call this same measure SNR, but I find that can be confused with terms we'll talk about in Chapter 5, SO I'll keep the notation SQNR.) SQNR refers to the ratio of the signal input power to the power of the error (or noise) introduced by the quantizer. Mathematically, it's described by (4.19) where X m is the average (or mean) X value. Because we want quantizers to have a small error, and the size of the error term appears on the denominator (bottom) of the SQNR term, it makes sense that engineers say "good quantizers have a large SQNR." A "Classic" To give you a better understanding of the overall measures mse and SQNR, what follows is a "classic" example of how to compute the mse and SQNR for a particular uniform quantizer. Let's say x is a uniformly distributed random variable between [a,b]; that is to say, Px (x) looks like Figure 4.16(a). A uniform quantizer is shown in the graph of Figure 4.16(b). Let's figure out the mse and SQNR of the quantizer for the given input signal and quantizer. First, the mse. As you'll recall, the equation for mse is given by (4.20) (4.21) Source Coding and Decoding: Making it Digital (b-a) a a+^ =a+ /2 Figure 4.16 (a) p(x) of quantizer input X (b) Graphical description of uniform quantizer Now, lookin