Comparative Analysis of Time Interval Stability in Cesium and Hydrogen Maser Clocks at 4 Minute and 12-Minute Sampling Rates

This study presents a comparative analysis of frequency stability in high-precision timekeeping systems, examining cesium atomic clocks and hydrogen maser clocks at different sampling intervals. We test whether shorter 4-minute intervals reveal more frequency noise than conventional 12-minute intervals. Using Allan deviation and power spectral density methods, we analyze phase and frequency data from multiple clock comparisons. Our approach applies polynomial prewhitening to remove deterministic trends and gap-filling algorithms to address anomalies, ensuring robust statistics. Results show distinct noise signatures between cesium and maser technologies across sampling rates. The analysis highlights dominant noise processes (white phase modulation, flicker frequency noise, random walk frequency modulation) and their dependence on interval length. Findings suggest higher sampling rates expose additional noise components averaged out at longer intervals. This research informs optimal sampling strategies for different clock technologies and advances understanding of noise in precision timekeeping, with implications for GNSS, radio astronomy, and fundamental physics experiments requiring high temporal stability.