ers. A quantizer is called a mid-tread if it has a 0 as one of its codewords (allowed output amplitudes). In other words, a quantizer is a mid-tread if it changes any ampli- tude very close to 0 into a 0. For example, let's say I scream out a number, and you map it to the closest integer between -5 and +5. If I scream 0.3, you say 0. If I shout -0.2, you shout 0. In this case, you're acting like a mid-tread quantizer. An example of a mid-tread quantizer is shown in Figure 4.14(a). A quantizer is called a mid-riser if it does not have 0 as one of its codewords. In other words, a quantizer is a mid-riser if it does NOT change amplitudes close to 0 into 0. For example, let's say I scream a number, and you shout back the nearest number ending in .5, between -5 and 5. I shout out "-0.3," and you reply with "-0.5." I shout out "0.4," and you yelp "0.5." In this case, you are acting like a mid-riser. An example of a mid-riser is shown in Figure 4.14(b). Figure 4.14 (a) Example of mid-tread quantizer (b) Example of mid-riser quantizer Chapter Four Figure 4.15 (a) Example of uniform quantizer (b) Example of non-uniform quantizer A quantizer is called uniform if all its codewords are equally spaced. For example, when I scream a number and you reply with the closest integer in 1 to 10, the possible codewords are 1, 2, 3, and SO on up to 10. These codewords are all spaced apart by the same distance (of 1), and SO this is a uniform quantizer. This type is shown in Figure 4.15(a). A quantizer is a non-uniform quantizer if all its codewords are NOT equally spaced. Let's say I shout out a number, and you reply with either 1, 3, 6, or 10, which- ever is closest. In this case, the codewords are not equally spaced, and SO you are acting as a non-uniform quantizer. This example is shown in Figure 4.15(b). Example 4.4 Looking at the quantizers in Figure E4.5, determine if they are mid-tread or mid- rise and if they are uniform or non-uniform. Solution: The quantizer in Figure E4.5(a): 1. has zero as one of its codewords, making it mi