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    Area of Science:

    • Electrical Engineering
    • Signal Processing
    • Physics

    Background:

    • Complex electronic systems rely on stable oscillators for functions like communication and navigation.
    • Oscillator stability is often described by Allan Variance (AVAR) in the time domain.
    • Power Spectral Density (PSD) in the frequency domain offers a more complete noise characterization, but conversion from AVAR to PSD is challenging.

    Purpose of the Study:

    • To develop an analytical method for converting AVAR/HVAR profiles into approximated PSDs.
    • To enable accurate simulation of complex noise across various noise types and combinations.
    • To validate the method using NASA's deep space atomic clock data.

    Main Methods:

    • An analytical algorithm was developed to approximate PSD from time-domain AVAR/HVAR power-law descriptions.
    • The method allows for unambiguous conversion from AVAR/HVAR to PSD, unlike previous approaches.
    • The algorithm's self-validation is achieved by reconstructing the AVAR/HVAR from the generated PSD.

    Main Results:

    • The study presents a straightforward method to generate PSDs from AVAR/HVAR data.
    • The method successfully generated multicolored noise for end-to-end simulations, validated with deep space atomic clock data.
    • Limitations and analytical expressions for a continuous version of the algorithm were also reported.

    Conclusions:

    • The developed method provides a robust way to translate time-domain oscillator stability measures (AVAR/HVAR) into frequency-domain descriptions (PSD).
    • This facilitates more accurate and comprehensive noise modeling in complex electronic systems, crucial for performance optimization.
    • The approach is broadly applicable, enhancing simulations for applications ranging from wireless communications to space navigation.