  We introduce DAYENU, a linear, spectral filter for HI intensity mapping that
achieves the desirable foreground mitigation and error minimization properties
of inverse co-variance weighting with minimal modeling of the underlying data.
Beyond 21 cm power-spectrum estimation, our filter is suitable for any analysis
where high dynamic-range removal of spectrally smooth foregrounds in
irregularly (or regularly) sampled data is required, something required by many
other intensity mapping techniques. Our filtering matrix is diagonalized by
Discrete Prolate Spheroidal Sequences which are an optimal basis to model
band-limited foregrounds in 21 cm intensity mapping experiments in the sense
that they maximally concentrate power within a finite region of Fourier space.
We show that DAYENU enables the access of large-scale line-of-sight modes that
are inaccessible to tapered DFT estimators. Since these modes have the largest
SNRs, DAYENU significantly increases the sensitivity of 21 cm analyses over
tapered Fourier transforms. Slight modifications allow us to use DAYENU as a
linear replacement for iterative delay CLEANing (DAYENUREST). We refer readers
to the Code section at the end of this paper for links to examples and code.

Cosmology and Nongalactic Astrophysics;Instrumentation and Methods for Astrophysics