been expressed as cylindrically binned power spectra. To form cylindrically binned power spectra, one begins with unbinned power spectra $P(\mathbf{k})$, where $\mathbf{k}$ is the three-dimensional wavevector of spatial Fourier modes. If the field of view is narrow, there exists a particular direction that can be identified as the line-of-sight (or radial) direction. One of the three components of $\mathbf{k}$ can then be chosen to lie along this direction and labeled $k_\parallel$ as a reminder that it is *parallel* to the line-of-sight. The remaining two components—which we arbitrarily designate $k_x$ and $k_y$ in this paper—describe transverse (i.e., angular fluctuations), and have a magnitude $k_\perp \equiv \sqrt{k_x^2 + k_y^2}$. Binning $P(\mathbf{k})$ along contours of constant $k_\perp$ gives $P(k_\perp, k_\parallel)$, the cylindrically binned power spectrum.

Expressing the power spectrum as a function of $k_\perp$ and $k_\parallel$ is a powerful diagnostic exercise because intensity mapping surveys probe line-of-sight fluctuations in a fundamentally different way than the way they probe angular fluctuations. Systematics are therefore usually anisotropic and have distinct signatures on the $k_\perp$-$k_\parallel$ plane [@morales_and_hewitt2004]. For example, cable reflections and bandpass calibration errors tend to appear as features parallel to the $k_\parallel$ axis [@dillon_et_al2015; @ewall-wice_et_al2016b; @jacobs_et_al2016]. Thus, the cylindrically binned power spectrum is a 