  Radio interferometers targeting the 21cm brightness temperature fluctuations
at high redshift are subject to systematic effects that operate over a range of
different timescales. These can be isolated by designing appropriate Fourier
filters that operate in fringe-rate (FR) space, the Fourier pair of local
sidereal time (LST). Applications of FR filtering include separating effects
that are correlated with the rotating sky vs. 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.
