Accuracy Analysis for a Single-Bit Simple Oversampled A/D Conversion in Shift Invariant Spaces

In this paper, we introduce a single-bit oversampled A/D (analog-to-digital) conversion scheme for signals in shift invariant spaces, which is very comparable to the simple oversampled A/D conversion theory for shift invariant spaces found in our previous work. In such a scheme, the decay rate of the quantization error e is surprisingly found to de-pend only on the smoothness of the dither function instead of the commonly believed generator. In particular, the quantization error behaves as kek21 = O( 2) if the dither function is Lipschitz-1 contin-uous. Moreover, the bit-rate required to encode the converted digital signal only increases as a logarithm of the sampling ratio. In addition, this scheme can be easily implemented in practice