Statistical analysis of amplitude-quantized sampled-data systems

QUANTIZATION, or round-off, occurs whenever physical quantities are represented numerically. The values of measurements may be designated by integers corresponding to their nearest numbers of units. Round-off errors have values between ±1/2 unit, and can be made small by choice of the basic unit. It is apparent, however, that the smaller the size of the unit, the larger will be the numbers required to represent the same physical quantities and the greater will be the difficulty and expense in storing and processing these numbers. Often, a balance has to be struck between accuracy and economy. In order to establish such a balance, it is necessary to have a means of evaluating quantitatively the distortion resulting from rough quantization. The analytical difficulty arises from the inherent nonlinearities of the quantization process.