Correlation Statistics of Quantized Noiselike Signals
Carl Gwinn · Publications of the Astronomical Society of the Pacific · 2003
I calculate the statistics of correlation of two digitized noiselike signals, which are drawn from complex Gaussian distributions, sampled, quantized, correlated, and averaged. Averaged over many such samples, the correlation r approaches a Gaussian distribution. The mean and variance of r fully characterize the distribution of r . The mean corresponds to the reproducible part of the measurement, and the variance corresponds to the random part, or noise. I investigate the case of nonnegligible covariance ρ between the signals. Noise in the correlation can increase or decrease, depending on quantizer parameters, when ρ increases. This contrasts with the correlation of continuously valued or unquantized signals, for which the noise in phase with ρ increases with increasing ρ, and noise out of phase decreases. Indeed, for some quantizer parameters, I find that the correlation of quantized signals provides a more accurate estimate of ρ than would correlation without quantization. I present analytic results in exact form and as polynomial expansions, and compare these mathematical results with results of computer simulations.