NMR spectroscopy is an inherently insensitive technique, and many challenging applications such as biomolecular studies operate at the very limits of sensitivity and resolution, Advances in superconducting magnet, cryogenic probe, and pulse sequence technologies have resulted in dramatic improvements in both sensitivity and resolution in the past decade. Conversely, the signal-processing method used most widely in NMR spectroscopy, extrapolation of the time domain signal by linear prediction (LP) followed by discrete Fourier transformation (DFT), was developed in the early 1980s and has not been subjected to detailed scrutiny for its impact on sensitivity and resolution. Here we report the first systematic investigation of the accuracy and precision of spectra obtained by LP extrapolation followed by DFT. We compare the results to spectra obtained by maximum-entropy (MaxEnt) reconstruction, which was developed contemporaneously to LP extrapolation but is not widely employed in NMR spectroscopy. Although it reduces truncation artifacts and increases the amplitudes of strong peaks, we find that LP extrapolation generates false-positive peaks and introduces frequency errors. These defects of LP extrapolation become less pronounced for longer data records and higher signal-to-noise ratio. MaxEnt generally yields more detectable peaks for a given number of data samples, more accurate peak frequencies, and fewer false-positive peaks than LIP extrapolation. MaxEnt also permits the use of nonlinear sampling, which can give dramatic improvements in resolution. These results show that the use of MaxEnt together with nonlinear sampling, rather than LP extrapolation, could reduce the amount of instrument time required for adequate sensitivity and resolution by a factor of 2 or more.