The R-R interval measurement from digitized electrocardiograms (ECG) contains an error due to the finite sampling frequency which may jeopardize the beat-to-beat analysis of the heart rate. In this paper, we develop a model to describe and quantitate this error. The "measured" R-R interval is modeled as the sum of the "true" R-R interval and of the error of measurement. The first and second order statistics of the error are computed in order to investigate its influence on the heart rate variability (HRV) power spectrum. They are found to be only functions of the ECG sampling frequency and, in particular, the power spectrum of the error contributes an additive high-pass filter-like term (colored noise) to the power spectrum of the HRV. The accuracy of the model is tested via a simulation procedure. The model indicates that the relative balance between the HRV and the error power spectra is important and should be checked before any variability analysis on the heart rate. This balance may be favorable to the error when 1) the sampling frequency of the ECG is too low, and/or 2) the variability of the heart rate is too little. In these cases, the HRV spectrum analysis may not give reliable results. Two tests are proposed in order to evaluate the error influence either in specific frequency bands or in the total frequency range.