Dither inputs are externally applied disturbances that have been used in control systems and in signal processing systems to alleviate the effects of nonlinearity, hysteresis, static friction, gear backlash, quantization, etc. In many cases, dither inputs have been used to “improve” system behavior without there being a clear idea of the nature of the improvement sought and without any method for designing the dither signal other than empiricism. It is the purpose of this chapter to explain the uses of dither signals in systems containing quantizers. We will employ the mathematical methods developed herein for the design of dither signals and for analysis of their benefits and limitations.

DITHER: ANTI-ALIAS FILTERING OF THE QUANTIZER INPUT CF

When the input signal to a uniform quantizer has statistical properties allowing it to satisfy QT I or QT II, the PQN model can be applied to describe the statistical behavior of the quantizer. This is a linear model, and from the point of view of moments and joint moments, the quantizer acts like a source of additive independent noise. This type of linear behavior would be highly desirable under many circumstances.

When the quantizer input is inadequate for satisfaction of QT II, it is possible to add an independent dither signal to the quantizer input so that the sum of input and dither does satisfy QT II. Then the quantizer exhibits linear behavior and we can say that it is linearized.