Structure Matters: Differentially Private Spectral Statistics for ECG Time Series

Releasing high-dimensional spectral summaries under differential privacy can introduce substantial error when every coordinate is perturbed. We ask whether preserving frequency structure improves utility beyond dimension reduction alone. Using electrocardiogram (ECG) recordings as a benchmark, we study window-level differentially private release of aggregate log-power spectral density (log-PSD) curves. Each window is mapped to a Welch log-PSD vector. The mechanism retains a publicly calibrated low-order discrete cosine transform (DCT) prefix, clips in the projected space, averages the resulting vectors, and adds Gaussian noise. We compare against full-dimensional Gaussian release, a dimension- and noise-matched random-DCT control, and five random DCT masks with independently calibrated clipping radii. On a frozen 16-record MIT-BIH test at the preselected evaluation setting, the structured release reduces median relative $L_2$ error by $39.6\%$ relative to the median independently calibrated random control and by $78.5\%$ relative to full-dimensional release. The random-control comparison provides evidence that preserving smooth variation across the frequency axis improves utility beyond compression alone.