Effects of Nonuniform Input Spectra on Signal-to-Noise Ratio in Wide-Bandwidth Digital Correlation

In a low-bit sampling digital correlator for wide-bandwidth interferometry observations, nonuniform spectra of the analog input can degrade the correlator efficiency. In this work we evaluate this issue in detail, particularly for correlators having fine spectral resolution. We find the degradation to be due to nonlinear transfer of noise among different frequency channels, thereby altering the per channel signal-to-noise ratio (S/N) in an unfavorable manner with low-power channels having worse S/N and high-power channels, better S/N. (The favorable S/N in high-power channels arise primarily from effective oversampling.) To the leading order, the favorable and unfavorable S/N at different channels can largely cancel and the S/N degradation occurs as a second-order effect. However, when the two input spectra for correlation deviate from each other, such a cancellation mechanism may be suppressed.