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The Tropospheric Emission Spectrometer (TES) on the Earth Observing System (EOS) Aura satellite measures the infrared radiance emitted by the Earth's surface and atmosphere using Fourier transform spectrometry. The measured interferograms are converted into geolocated, calibrated radiance spectra by the L1 (Level 1) processing, and are the inputs to L2 (Level 2) retrievals of atmospheric parameters, such as vertical profiles of trace gas abundance. We describe the algorithmic components of TES Level 1 processing, giving examples of the intermediate results and diagnostics that are necessary for creating TES L1 products. An assessment of noise-equivalent spectral radiance levels and current systematic errors is provided. As an initial validation of our spectral radiances, TES data are compared to the Atmospheric Infrared Sounder (AIRS) (on EOS Aqua), after accounting for spectral resolution differences by applying the AIRS spectral response function to the TES spectra. For the TES L1 nadir data products currently available, the agreement with AIRS is 1 K or better.