Autocorrelation-Based Heart Rate Estimation
Autocorrelation heart rate estimation exploits the quasi-periodic nature of PPG by computing the signal's correlation with time-shifted copies of itself. The lag at the first significant autocorrelation peak corresponds to the dominant cardiac period, providing heart rate estimates that are inherently robust to waveform morphology changes.
The autocorrelation function R(τ) = Σ x(n)·x(n+τ) measures self-similarity at lag τ. For a periodic PPG signal with period T (cardiac cycle), R(τ) exhibits peaks at τ = T, 2T, 3T, etc. Heart rate is estimated as HR = 60/T bpm. The first peak after the central peak (at τ = 0) gives the fundamental period, with the search range constrained to 0.25–2 seconds (30–240 bpm).
Autocorrelation is computationally cheaper than FFT for short segments (O(N·M) where M is the lag range vs. O(N log N) for FFT) and provides direct time-domain periodicity estimation without spectral leakage or windowing artifacts. It is particularly robust to amplitude modulation (respiratory variation) and waveform shape changes because it measures timing similarity rather than spectral content.
Average magnitude difference function (AMDF), a variant that computes the average absolute difference instead of correlation, provides similar periodicity detection with lower computational cost and is widely used in embedded PPG firmware. Combined autocorrelation-AMDF approaches use AMDF for coarse period estimation and autocorrelation for refinement, achieving 1–3 bpm accuracy during rest and light activity.
Frequently Asked Questions
How does autocorrelation compare to FFT for PPG heart rate?
Autocorrelation provides direct time-domain period estimates without spectral resolution limitations. FFT provides better frequency discrimination when multiple periodic components are present. Autocorrelation is more robust to short segments (<5 seconds).
What window length is needed for autocorrelation HR estimation?
Minimum 3 seconds (capturing at least 2 cardiac cycles at 40 bpm). Optimal is 5–8 seconds for stable estimates. Unlike FFT, autocorrelation does not benefit significantly from longer windows beyond 2–3 cycle periods.
Can autocorrelation handle irregular rhythms like AF?
Autocorrelation peak height decreases with rhythm irregularity. During AF, the autocorrelation peak is broader and lower, providing less precise but still usable period estimates. Peak height itself serves as a rhythm regularity index.