Fast estimation of higher-order moments using sign bit and reference signals

High data-rate signals pose challenging problems, e.g., in efficient computation of their autocorrelation and spectra. One popular technique exploits dithering and sign bit processing: here the band-limited analog signal is dithered by the addition of a discrete-time reference signal, which is then clipped to 1 bit; the resulting antipodal binary sequence is then used to obtain an estimate of the autocorrelation and spectra of the signal. We extend the notion to cross-moments of arbitrary orders and signals; this problem arises in several applications, such as radio astronomy and laser spectroscopy. We show that if the reference signal is stochastic, it must be uniformly distributed, and if it is non-random, it must again be uniformly distributed in a sense described. Closed form expressions are obtained for the variance of the cross-moments estimated from the resulting sign bit sequence. We also consider the M-level quantization scheme. The theory is corroborated by simulations.