This chapter begins by describing how the development of pulsed Fourier transform NMR revolutionized NMR, particularly with respect to acquisition of ¹³C spectra and the development of multiple pulse sequences. A simple one-pulse experiment for the acquisition of free induction decay signals is described, with emphasis on how the duration of the pulse determines the frequency width that is excited by the pulse. The free induction decay signal and the related frequency spectrum of a single off-resonance peak is used to illustrate the Fourier relationship between time and frequency response. In subsequent sections, all key factors on digital data acquisition and processing are covered. Topics covered include the central role of analog to digital convertors, digital oversampling, alternative forms of quadrature detection to distinguish between positive and negative frequencies, and analog versus digital noise filtration. Finally, the significance of partial saturation when acquiring multi-scan spectra is highlighted and the relative merits of using a relaxation delay or a reduced pulse angle to minimize partial saturation is discussed.