Sampling rate and the estimation of ensemble variability for repetitive signals

The measurement of ensemble variability in time-aligned event signals is studied in relation to sampling rate requirements. The theoretical analysis is based on statistical modelling of time misalignment in which the time resolution is limited by the length of the sampling interval. For different signal-to-noise ratios (SNRs), the sampling rate is derived which limits the misalignment effect to less than 10% of the noise effect. Each signal is assumed to be corrupted by additive noise. Using a normal QRS complex with a high SNR (≈ 30 dB), a sampling rate of approximately 3 kHz is needed for accurate ensemble variability measurements. This result is surprising since it implies that the Nyquist rate is far too low for accurate variability measurements. The theoretical results are supplemented with results obtained from an ECG database of 94 subjects for which the ensemble variability is computed at different sampling rates using signal interpolation. The ensemble variability is substantially reduced (40%) when increasing the rate from 1 to 3 kHz, thus corroborating the results suggested by the theoretical analysis.