Single-Bit Oversampled A/D Conversion With Exponential Accuracy in the Bit Rate

A scheme for simple oversampled analog-to-digital (A/D) conversion using single-bit quantization is presented. The scheme is based on recording positions of zero-crossings of the input signal added to a deterministic dither function. This information can be represented in a manner such that the bit rate increases only logarithmically with the oversampling factor r. The input band-limited signal can be reconstructed from this information locally with O(1/r) pointwise error, resulting in an exponentially decaying distortion-rate characteristic. In the course of studying the accuracy of the proposed A/D conversion scheme, some new results are established about reconstruction of band-limited signals from irregular samples using linear combination of functions with fast decay. Schemes for local interpolation of band-limited signals from quantized irregular samples are also proposed.