The non-linearity in amplitude quantization can be smoothed by adding dither, or external noise-type signal to the input of a linear quantizer followed by an estimation filter. Although the optimum type of dither for a linear quantizer, or quantizer with uniform steps, is known to be one whose probability characteristic function must be band-limited in the "quantization frequency" domain, it is shown in this thesis that such a dither is physically unrealizable. In continuous or sampled-data systems with random inputs, one is often more interested in obtaining output averages and correlation estimates rather than finding the probability density of the input. In such cases the uniform density dither turns out to be optimum but not necessarily unique.
Dithers with three types of probability densities, namely, uniformly distributed (triangular waveforms included), Gaussian and that of a sinusoidal waveform are examined and compared. The constraints and performances of these dithers are further investigated using a PDP-8 small computer and its peripheral equipment at Carleton. A 3-bit quantizer system with dithering is shown to yield performance comparable to that of a 7-bit quantizer.