| The goal in digital device design is to achieve high performance at low cost, and to pursue this goal, all components of the device must be designed accordingly. A principal component common in digital devices is the quantizer, and frequently used is the minimum mean-squared error (MSE) or optimal , fixed-rate scalar quantizer. In this thesis, we focus on aids to the design of such quantizers.;For an exponential source with variance sigma2, we estimate the largest finite quantization threshold by providing upper and lower bounds which are functions of the number of quantization levels N. The upper bound is 3sigma log N, N ≥ 1, and the lower bound is 3sigma log N + oN (1) sigma - 1.46004sigma, N > 9. Using these bounds, we derive an upper bound to the convergence rate of N 2D (N) to the Panter-Dite constant, where D (N) is the least MSE of any N-level scalar quantizer. Furthermore, we present two, very simple, non-iterative and non-recursive suboptimal quantizer design methods for exponential sources that produce quantizers with good MSE performance.;For an improved understanding of the half steps and quantization thresholds in optimal quantizers as functions of N, we use as inspiration the result by Nitadori [19] where, exploiting a key side effect of the source's memoryless property, he derived an infinite sequence such that for any N, the kth term of the sequence is equal to the kth half step (counting from the right) of the optimal N -level quantizer designed for a unit variance exponential source. In our work, using an asymptotic version of this key side effect which holds for general exponential (GE) sources parameterized by an exponential power p and a utilizing a method of our own devising, we show that for such a source, the kth half step of an optimal N -level quantizer multiplied by the (p - 1)st power of the kth threshold approaches the kth term of the Nitadori sequence as N grows to infinity. Thus, the Nitadori sequence asymptotically characterizes the cells of MMSE quantizers for GE-sources, as well as exponential. |
