SIGN-BIT AMPLITUDE RECOVERY IN GAUSSIAN NOISE

摘要

Sign-bit amplitude recovery implies the recovery of signal from the average of the sign-bits of signal plus noise. We show that, given a Gaussian noise density, the average of the sign-bits of signal plus noise is not the signal, but is the Gauss error function with an argument that is proportional to the signal and inversely proportional to the standard deviation of the noise. This result can appear to provide amplitude recovery by producing a facsimile of the signal but the signal is only properly recovered by processing the data with the inverse error function. Based on the Central Limit Theorem, the optimal signal-to-noise ratio for amplitude recovery in Gaussian noise is identical to that of uniform noise, S/N = 1. This theory is tested using computer simulations with synthetic signal and noise. First, we demonstrate sign-bit amplitude recovery in uniform noise. Next, we compare the sign-bit average in uniform noise with the sign-bit average in Gaussian noise before and after the inverse error function is applied. Finally we compare hard clipping in uniform noise to soft clipping in Gaussian noise which occurs for large signal-to-noise ratios.