  The discovery and study of pulsars and Fast Radio Bursts (FRBs) in
time-domain radio data is often hampered by radio frequency interference (RFI).
Some of this terrestrial RFI is impulsive and bright, and relatively easy to
identify and remove. Other anthropogenic signals, however, are weaker yet
periodic, and their persistence can drown out astrophysical signals. Here we
show that Fourier-domain excision of periodic RFI is an effective and powerful
step in detecting weak cosmic signals. We find that applying the method
significantly increases the signal-to-noise ratio of transient as well as
periodic pulsar signals. In live studies, we detected single pulses from
pulsars and FRBs that would otherwise have remained buried in background noise.
We show the method has no negative effects on pulsar pulse shape and that it
enhances timing campaigns. We demonstrate the method on real-life data from a
number of large radio telescopes, and conclude that Fourier-domain RFI excision
increases the effective sensitivity to astrophysical sources by a significant
fraction which can be even larger than an order of magnitude in case of strong
RFI. An accelerated implementation of the method runs on standard time-domain
radio data formats and is publicly available.
