 N amplitudes, it is often denoted mathematically by writing C = {y1,y2,..., YN}. In the example of Carl speaking a number, and you, the quantizer, speaking back the closest integer between 1 and 10, the codebook is simply C = {1,2,...,10}. Next, there's the word codeword, yi The codeword, Yi, simply refers to the ith of the N output amplitudes allowed by the quantizer. In the example of the reader as quantizer (speaking back the closest integer between 1 and 10), the codeword would be 1, the codeword y2 would be 2, and SO on. Next is the word cell, R.. The cell R refers to the set of input amplitudes that are mapped to the codeword yi. For example, consider the case of the reader (as quan- tizer) shouting back the closest integer between 1 and 10. If I say 7.6, the reader screams back 8. If I say 8.3, the reader again shouts back 8. In fact, any number in the set of numbers [7.5, 8.5) is mapped by the reader to the number 8. Hence, the set [7.5, 8.5) forms a cell. Since this cell corresponds to the amplitudes mapped to y's = 8, this cell is called R8 Simple. There are two types of cells, granular cells and overload cells. A granular cell refers to a cell that is bounded. For example, consider the cell R8 from the previous paragraph, which you'll recall was R8 =[7.5,8.5). = Because this cell consists of a set of numbers that do not stretch out to either plus or minus infinity, it is called a granular cell. Source Coding and Decoding: Making it Digital An overload cell, on the other hand, refers to a cell that is unbounded. Consider the example of Carl screaming a number, and you screaming back the nearest integer in 1 to 10. I say 9.7, you say 10. I say 10.2, you say 10. I say 100.67, you say 10. I say 100,000, you say 10. From this, you can tell that the cell for the number 10 consists of [9.5,00 ). Because this cell ends with 8 , it is called an overload cell. Types of Quantizers Not only do we telecommunication engineers have words to describe any quantizer, but we also have words to help us categorize quantiz