High quality A/D conversion using single-bit quantizers: a novel approach based on generalized frequency modulation

The problem of constructing high resolution analog-to-digital converters using a single-bit quantizer is addressed and a new approach is outlined which expands the bandwidth of the signal prior to quantization. It is shown that the efficiency of the quantizer is related to the “orthant-visiting” capability of the bandwidth expansion map. When frequency modulation is used to expand the bandwidth, the noise power is shown to decay as O(1/r²), where r is the number of times a single-bit quantizer is used per Nyquist sample. We then introduce exponential chirp modulation and show that this leads to exponential decay of the noise power with r. Finally we show that the exponential chirp-based system can be realized using a system of differential equations