2025/01/02 by Neil Irwin Bernardo, Bernardo, Neil Irwin, Shaik Basheeruddin Shah +3 · 3 citations
Engineering · Decision Sciences · Computer Science · #Fault Detection and Control Systems #Advanced Statistical Process Monitoring #Machine Learning and Algorithms
paper · pdf · doi:10.48550/arxiv.2501.01506
In this paper, we investigate the relationship between the dynamic range and quantization noise power in modulo analog-to-digital converters (ADCs). Two modulo ADC systems are considered: (1) a modulo ADC which outputs the folded samples and an additional 1-bit folding information signal, and (2) a modulo ADC without the 1-bit information. A recovery algorithm that unfolds the quantized modulo samples using the extra 1-bit folding information is analyzed. Using the dithered quantization framework, we show that an oversampling factor of OF > 3 and a quantizer resolution of b > 3 are sufficient conditions to unfold the modulo samples. When these conditions are met, we demonstrate that the mean squared error (MSE) performance of modulo ADC with an extra 1-bit folding information signal is better than that of a conventional ADC with the same number of bits used for amplitude quantization. Since folding information is typically not available in modulo ADCs, we also propose and analyze a recovery algorithm based on orthogonal matching pursuit (OMP) that does not require the 1-bit folding information. In this case, we prove that OF > 3 and b > 3 + log2(δ) for some δ> 1 are sufficient conditions to unfold the modulo samples. For the two systems considered, we show that, with sufficient number of bits for amplitude quantization, the mean squared error (MSE) of a modulo ADC is O((1)/(OF3)) whereas that of a conventional ADC is only O((1)/(OF)). We extend the analysis to the case of simultaneous acquisition of weak and strong signals occupying different frequency bands. Finally, numerical results are presented to validate the derived performance guarantees.