Corentin Ravoux, Marie-Lynn Abdul-Karim, Jean-Marc Le Goff, Eric Armengaud, Jessica N. Aguilar, Steven Ahlen, Stephen Bailey, Davide Bianchi, Allyson Brodzeller, David Brooks, Jonás Chaves-Montero, Todd Claybaugh, Andrei Cuceu, Roger de Belsunce, Axel de la Macorra, Arjun Dey, Zhejie Ding, Peter Doel, Simone Ferraro, Andreu Font-Ribera, Jaime E. Forero-Romero, Enrique Gaztañaga, Naim Göksel Karaçaylı, Satya Gontcho A Gontcho, Gaston Gutierrez, Julien Guy, Hiram K. Herrera-Alcantar, Mustapha Ishak, Robert Kehoe, David Kirkby, Theodore Kisner, Anthony Kremin, Martin Landriau, Laurent Le Guillou, Michael E. Levi, Marc Manera, Paul Martini, Aaron Meisner, Ramon Miquel, Paulo Montero-Camacho, Andrea Muñoz-Gutiérrez, Seshadri Nadathur, Gustavo Niz, Nathalie Palanque-Delabrouille, Zhiwei Pan, Will J. Percival, Ignasi Pérez-Ràfols, Matthew M. Pieri, Francisco Prada, Graziano Rossi, Eusebio Sanchez, Christoph Saulder, David Schlegel, Michael Schubnell, Hee-Jong Seo, Joseph H. Silber, Małgorzata Siudek, David Sprayberry, Ting Tan, Ji-Jia Tang, Gregory Tarlé, Michael Walther, Benjamin A. Weaver, Christophe Yèche, Jiaxi Yu, Rongpu Zhou, Hu Zou

We present the one-dimensional Lyman-alpha forest power spectrum measurement derived from the data release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI). The measurement of the Lyman-alpha forest power spectrum along the line of sight from high-redshift quasar spectra provides information on the shape of the linear matter power spectrum, neutrino masses, and the properties of dark matter. In this work, we use a Fast Fourier Transform (FFT)-based estimator, which is validated on synthetic data in a companion paper. Compared to the FFT measurement performed on the DESI early data release, we improve the noise characterization with a cross-exposure estimator and test the robustness of our measurement using various data splits. We also refine the estimation of the uncertainties and now present an estimator for the covariance matrix of the measurement. Furthermore, we compare our results to previous high-resolution and eBOSS measurements. In another companion paper, we present the same DR1 measurement using the Quadratic Maximum Likelihood Estimator (QMLE). These two measurements are consistent with each other and constitute the most precise one-dimensional power spectrum measurement to date, while being in good agreement with results from the DESI early data release.