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Limited Live-time Measurements of Frequency Spectra



David A. Howe, Neil Ashby, Danielle G. Lirette, Archita Hati, Craig W. Nelson


Frequency-difference-of-arrival (FDOA) can be used to monitor and track an emitter’s location by observing Doppler frequency shifts of the carrier during short pulsed transmissions. This specific application needs to consider two frequency-stability levels: the short Τon-average frequency measurements and the sampling time interval between measurements, denoted by Τs. We show the advantage of using “dynamic” ThêoH for τon frequency measurements. Between Τon transmissions while powered off, the emitter’s reference-oscillator frequency will change due to power-start thermal variations, vibration, stress, and other frequency disturbances. If we regard long-term frequency instability as an uncertainty on an oscillator's expected or designated frequency, then the dominant error of frequency prediction is likely to be the error due to frequency drift and/or random-walk FM, indicating the non-stationary behavior or disturbances. A two-sample variance is devised, called “Psi-variance,” that has desirable statistical properties similar to the Allan variance. From this, we compute the power spectral density of frequency fluctuations, Sy(f), from which one can get phase noise, L(f).
Proceedings Title
Proceedings of the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum
Conference Dates
May 1-5, 2011
Conference Location
San Fancisco, CA


Frequency Stability, Dead Time, Variance, Phase Noise, Dynamic variance, TCXO, Psi, Allan, Theo


Howe, D. , Ashby, N. , Lirette, D. , Hati, A. and Nelson, C. (2011), Limited Live-time Measurements of Frequency Spectra, Proceedings of the 2011 Joint IEEE International Frequency Control Symposium and European Frequency and Time Forum, San Fancisco, CA (Accessed June 19, 2024)


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Created July 31, 2011, Updated February 19, 2017