A study of the precision in the estimate of peak positions in spectroscopy was carried out. This study was carried out by considering both instrumental noise and error due to a finite digitization rate. Different strategies for estimating peak position were compared. The comparison showed that it is always desirable to use some form of curve fitting the peak rather than using the position of the digital maximum as the peak position estimate. It was shown that it is very difficult to estimate changes in peak position that are less than ten percent of the line width. A method for the estimation of peak areas for nuclear Overhauser enhancement factors was developed. Although this study constituted a preliminary investigation, which did not directly consider all sources of error, it was found that the peak area can be determined with high precision in the presence of substantial phase error. This method (called the product method) involves multiplying the peak height with the width at one-half peak height to compute peak area.