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Synthetic data sets are used in cosmology to test analysis procedures, toverify that systematic errors are well understood and to demonstrate thatmeasurements are unbiased. In this work we describe the methods used togenerate synthetic datasets of Lyman-$\alpha$ quasar spectra aimed for studieswith the Dark Energy Spectroscopic Instrument (DESI). In particular, we focuson demonstrating that our simulations reproduces important features of realsamples, making them suitable to test the analysis methods to be used in DESIand to place limits on systematic effects on measurements of Baryon AcousticOscillations (BAO). We present a set of mocks that reproduce the statisticalproperties of the DESI early data set with good agreement. Additionally, we usefull survey synthetic data to forecast the BAO scale constraining power withDESI.

Synthetic spectra for Lyman-$\alpha$ forest analysis in the Dark Energy Spectroscopic Instrument