Detection of sub-threshold oscillations in the presence of strong signals

Abstract

This paper reports the performance of sinusoid-crossing (SC) sampling method in detecting sub-threshold oscillations in the presence of a strong sinusoid. Unlike the conventional sampling procedure, which gives the sampled version of a signal using its amplitude representation, the sinusoid-sampling method represents the signal via the sequence of 2M locations {t_i} where the input signal s(t) crosses the reference sinusoid r(t) = A_rcos(2πf_rt) of frequency f_r = M = 512 within the sampling period T = 1. From these crossing locations, the discrete Fourier spectrum can be computed directly which is an important tool in signal processing. Also, the SC detector is easier to implement on hardware because it employs only the use of a single comparator. The presence of a threshold or a detection limit B in the sinusoid-sampling method is brought about by the finite accuracy in determining the 2M locations {t_i} within a sampling interval T/2M = 1/2M. The sequence representing the sinusoid-crossing (SC) locations of a weak signal of interest S_W(t)= A_Wcos(2πf_Wt) whose amplitude A_W is less than (B = A_rπ/2N), where N is the number of possible locations in one sampling interval, is similar to that of a zero signal. It has been shown that adding noise, termed as dither noise, to signals prior to detection enhances the dynamic range for both the conventional analog-to-digital converter (ADC) and the sinusoid-crossing detector, such that normally-undetectable signals are rendered detectable. This paper addresses the issue of whether adding a deterministic signal S_S(t)= A_Scos(2πf_St) rather than random dither noise to the undetectable sinusoid prior to detection affects the SNR gain.