ABSTRACT


Onebit quantization is a method of representing bounded signals by {+1,1} sequences that are computed from regularly spaced samples of these signals; as the sampling density is increased, convolving these onebit sequences with appropriately chosen averaging kernels must produce increasingly close approximations of the original signals. This method is widely used for analogtodigital conversion because of the many advantages its implementation presents over the classical and more familiar method of fineresolution quantization. A striking feature of onebit quantization is that all bits are given equal importance. This brings challenges with it, one of which is to achieve high accuracy. A fundamental open problem is the determination of the best possible behavior of the approximation error as a function of the sampling density for various function classes, and most importantly for the class of bandlimited functions, which is a model space for audio signals. Some of the other open problems ask for precise error estimates for particular popular algorithms used in practice. In this talk, we present the recent progress towards the solution of these problems, and the interplay of various types of mathematics in achieving these results. Return to Applied Math Colloquium home page 