Shaping the quantization noise in high resolution digital spectroscopy : theory and experiments

By using error feedback in analog to digital converters (ADCs) it is possible to shape the quantization noise spectral density. In particular, with delta sigma (\u394\u3a3) oversampling ADCs, the quantization noise is pushed towards high frequencies, where it is digitally filtered out. In this paper, we theoretically discuss and experimentally verify by using a low-cost, commercial ADC for audio applications, the suitability of actual \u394\u3a3 ADCs in high-resolution spectroscopy. The beneficial effects of noise shaping result in a 7 bits increase of the original ADC resolution. The effects of the correlation between noise and signal amplitude are measured and their importance are shown to be reduced by sampling the output waveform of a spectroscopy amplifier instead of its constant peak level. The optimum filter for maximizing the much greater than twice the bandwidth of the signal signal-to-quantization-noise ratio is derived and its use yields an experimental increase of 1 bit of the achievable resolution. These ADCs could be integrated in a digital integrated circuit with ease, thus opening the way for a completely integrated spectroscopy system