Full recovery of subthreshold bandlimited signals with a 1.5 bit analog-to-digital converter

Abstract

Additive noise has been shown to have the counterintuitive effect of enhancing the dynamic response of a non-linear system to an input stimulus instead of degrading it. In stochastic resonance, noise is added to the weak or subthreshold (undetectable) sinusoid prior to its detection by a threshold detector. The unknown sinusoid frequency is ascertained from the peak that is produced in the power spectrum, which is calculated from the Fourier transform of the autocorrelation of the detector output over time. A plot of the signal-to-noise (SNR) of the spectral peak reveals that its value first achieves a maximum with increasing noise variance before finally decreasing at larger noise amplitudes.
Current approaches in noise-aided detection do not allow for the full recovery of the weak bandlimited signals. The stochastic resonance (SR) approach is only useful with sinusoids and could reveal only its frequency and a good estimate of its amplitude but not its phase because the power spectrum does not contain such information.
In this paper, we demonstrate a new method for recovering a stationary sub-threshold multifrequency (bandlimited) signal from the output of a 1.5 bit analog-to-digital converter (ADC) which consists of two comparators (on/off outputs) in parallel. We also show that the response of the signal quality measures such as Linfoot's criteria compared to noise exhibits a peak similar to the SR effect.