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Radio interferometers targeting the 21cm brightness temperature fluctuations at high redshift are subject to systematic effects that operate over a range of different time-scales. These can be isolated by designing appropriate Fourier filters that operate in fringe-rate (FR) space, the Fourier pair of local sidereal time. Applications of FR filtering include separating effects that are correlated with the rotating sky versus those relative to the ground, down-weighting emission in the primary beam sidelobes, and suppressing noise. FR filtering causes the noise contributions to the visibility data to become correlated in time, however, making interpretation of subsequent averaging and error estimation steps more subtle. In this paper, we describe fringe-rate filters that are implemented using discrete prolate spheroidal sequences, and designed for two different purposes–beam sidelobe/horizon suppression (the 'mainlobe' filter), and ground-locked systematics removal (the 'notch' filter). We apply these to simulated data, and study how their properties affect visibilities and power spectra generated from the simulations. Included is an introduction to fringe-rate filtering and a demonstration of fringe-rate filters applied to simple situations to aid understanding. [ABSTRACT FROM AUTHOR]

Power spectrum estimators are an important tool in efforts to detect the 21 cm brightness temperature fluctuations from neutral hydrogen at early times. An initial detection will likely be statistical in nature, meaning that it will not be possible to make a coherent map of the brightness temperature fluctuations; instead, only their variance will be measured against a background of noise and residual systematic effects. Optimal quadratic estimator-based methods often apply an inverse covariance weighting to the data. However, inaccurate covariance modelling can lead to reduced sensitivity and, in some cases, severe signal loss. We recently proposed a Bayesian method to jointly estimate the 21 cm fluctuations, their power spectrum, and foreground emission. Instead of requiring a fixed a priori estimate of the covariance, we estimate the covariance as part of the inference. Choices of parametrization, particularly of the foregrounds, are subject to model errors and could lead to biases and other ill effects if not properly controlled. In this paper, we investigate the effects of inaccurate foreground models on 21 cm power spectrum recovery. Using simulated visibilities, we find that, even in the most extreme scenarios tested, our approach is capable of recovering 21 cm delay power spectrum estimates consistent with a known input signal for delays |$\gtrsim 300$| ns (⁠|$\sim$| 88 per cent of the available Fourier modes). This is true even when using foreground models derived from modified foreground catalogues containing spatial and spectral perturbations at the quoted level of uncertainty on our foreground catalogues. [ABSTRACT FROM AUTHOR]