A spectral synthesis method to suppress aliasing and calibrate for delay errors in Fourier transform correlators

TL;DR

This paper introduces a software-based spectral synthesis method that suppresses aliasing and calibrates delay errors in Fourier transform correlators, improving spectral accuracy in radio interferometry.

Contribution

It presents a novel oversampling technique that reconstructs the cross-correlation function, reducing aliasing and accounting for delay errors in Fourier transform correlators.

Findings

Successfully suppresses aliasing in simulations

Robustly accounts for delay errors

Produces regularly gridded spectral channels

Abstract

Context: Fourier transform (or lag) correlators in radio interferometers can serve as an efficient means of synthesising spectral channels. However aliasing corrupts the edge channels so they usually have to be excluded from the data set. In systems with around 10 channels, the loss in sensitivity can be significant. In addition, the low level of residual aliasing in the remaining channels may cause systematic errors. Moreover, delay errors have been widely reported in implementations of broadband analogue correlators and simulations have shown that delay errors exasperate the effects of aliasing. Aims: We describe a software-based approach that suppresses aliasing by oversampling the cross-correlation function. This method can be applied to interferometers with individually-tracking antennas equipped with a discrete path compensator system. It is based on the well-known property of interferometers where the drift scan response is the Fourier transform of the source's band-limited spectrum. Methods: In this paper, we simulate a single baseline interferometer, both for a real and a complex correlator. Fringe-rotation usually compensates for the phase of the fringes to bring the phase centre in line with the tracking centre. Instead, a modified fringe-rotation is applied. This enables an oversampled cross-correlation function to be reconstructed by gathering successive time samples. Results: Simulations show that the oversampling method can synthesise the cross-power spectrum while avoiding aliasing and works robustly in the presence of noise. An important side benefit is that it naturally accounts for delay errors in the correlator and the resulting spectral channels are regularly gridded.