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

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <emphasis><formula formulatype="inline"> <tex>$r$</tex></formula></emphasis>. The input band-limited signal can be reconstructed from this information locally with <emphasis><formula formulatype="inline"> <tex>$O(1/r)$</tex></formula></emphasis> pointwise error, resulting in an exponentially decaying distortion-rate characteristic. </para>