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We present the power spectrum methodology used for the first-season COMAP analysis, and assess the quality of the current data set. The main results are derived through the Feed-feed Pseudo-Cross-Spectrum (FPXS) method, which is a robust estimator with respect to both noise modeling errors and experimental systematics. We use effective transfer functions to take into account the effects of instrumental beam smoothing and various filter operations applied during the low-level data processing. The power spectra estimated in this way have allowed us to identify a systematic error associated with one of our two scanning strategies, believed to be due to residual ground or atmospheric contamination. We omit these data from our analysis and no longer use this scanning technique for observations. We present the power spectra from our first season of observing and demonstrate that the uncertainties are integrating as expected for uncorrelated noise, with any residual systematics suppressed to a level below the noise. Using the FPXS method, and combining data on scales $k=0.051-0.62 \,\mathrm{Mpc}^{-1}$ we estimate $P_\mathrm{CO}(k) = -2.7 \pm 1.7 \times 10^4\mu\textrm{K}^2\mathrm{Mpc}^3$, the first direct 3D constraint on the clustering component of the CO(1-0) power spectrum in the literature., Comment: Paper 4 of 7 in series. 18 pages, 11 figures, as accepted in ApJ

We describe the first season COMAP analysis pipeline that converts raw detector readouts to calibrated sky maps. This pipeline implements four main steps: gain calibration, filtering, data selection, and map-making. Absolute gain calibration relies on a combination of instrumental and astrophysical sources, while relative gain calibration exploits real-time total-power variations. High efficiency filtering is achieved through spectroscopic common-mode rejection within and across receivers, resulting in nearly uncorrelated white noise within single-frequency channels. Consequently, near-optimal but biased maps are produced by binning the filtered time stream into pixelized maps; the corresponding signal bias transfer function is estimated through simulations. Data selection is performed automatically through a series of goodness-of-fit statistics, including $\chi^2$ and multi-scale correlation tests. Applying this pipeline to the first-season COMAP data, we produce a dataset with very low levels of correlated noise. We find that one of our two scanning strategies (the Lissajous type) is sensitive to residual instrumental systematics. As a result, we no longer use this type of scan and exclude data taken this way from our Season 1 power spectrum estimates. We perform a careful analysis of our data processing and observing efficiencies and take account of planned improvements to estimate our future performance. Power spectrum results derived from the first-season COMAP maps are presented and discussed in companion papers., Comment: Paper 3 of 7 in series. 26 pages, 23 figures, submitted to ApJ