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We present the one-dimensional Lyman-$\alpha$ forest power spectrummeasurement using the first data provided by the Dark Energy SpectroscopicInstrument (DESI). The data sample comprises $26,330$ quasar spectra, atredshift $z > 2.1$, contained in the DESI Early Data Release and the first twomonths of the main survey. We employ a Fast Fourier Transform (FFT) estimatorand compare the resulting power spectrum to an alternative likelihood-basedmethod in a companion paper. We investigate methodological and instrumentalcontaminants associated to the new DESI instrument, applying techniques similarto previous Sloan Digital Sky Survey (SDSS) measurements. We use synthetic databased on log-normal approximation to validate and correct our measurement. Wecompare our resulting power spectrum with previous SDSS and high-resolutionmeasurements. With relatively small number statistics, we successfully performthe FFT measurement, which is already competitive in terms of the scale range.At the end of the DESI survey, we expect a five times larger Lyman-$\alpha$forest sample than SDSS, providing an unprecedented precise one-dimensionalpower spectrum measurement.

The Dark Energy Spectroscopic Instrument: One-dimensional power spectrum from first Lyman-$\alpha$ forest samples with Fast Fourier Transform