  Observations of 21cm line from neutral hydrogen promise to be an exciting new
probe of astrophysics and cosmology during the Cosmic Dawn and through the
Epoch of Reionization (EoR) to when dark energy accelerates the expansion of
the Universe. At each of these epochs, separating bright foregrounds from the
cosmological signal is a primary challenge that requires exquisite calibration.
In this paper, we present a new calibration method called nucal that extends
redundant-baseline calibration, allowing spectral variation in antenna
responses to be solved for by using correlations between visibilities measuring
the same angular Fourier modes at different frequencies. By modeling the
chromaticity of the beam-weighted sky with a tunable set of discrete prolate
spheroidal sequences (DPSS), we develop a calibration loop that optimizes for
spectrally smooth calibrated visibilities. Crucially, this technique does not
require explicit models of the sky or the primary beam. With simulations that
incorporate realistic source and beam chromaticity, we show that this method
solves for unsmooth bandpass features, exposes narrowband interference
systematics, and suppresses smooth-spectrum foregrounds below the level of 21cm
reionization models, even within much of the so-called "wedge" region where
current foreground mitigation techniques struggle. We show that this foreground
subtraction can be performed with minimal cosmological signal loss for certain
well-sampled angular Fourier modes, making spectral-redundant calibration a
promising technique for current and next-generation 21cm intensity mapping
experiments.
