Abstract
Oscillators and atomic clocks, as well as lasers and masers, are affected by physical mechanisms causing amplitude fluctuations, phase noise, and frequency instabilities. The physical properties of the elements composing the oscillator as well as external environmental conditions play a role in the coherence of the oscillatory signal produced by the device. Such instabilities demonstrate frequency drifts, modulation, and spectrum broadening and are observed to be nonstationary processes in nature. Most of the tools which are being used to measure and characterize oscillator stability are based on signal processing techniques, assuming time invariance within a temporal window, during which the signal is assumed to be stationary. This letter proposes a new time-frequency approach for the characterization of frequency sources. Our technique is based on the Wigner–Ville time-frequency distribution, which extends the spectral measures to include the temporal nonstationary behavior of the processes affecting the coherence of the oscillator and the accuracy of the clock. We demonstrate the use of the technique in the characterization of nonstationary phase noise in oscillators.
Highlights
In recent years, due to the high data rates required to be transferred in communication networks, the demand for highaccuracy satellite navigation systems and the development of high-resolution radars, oscillators, and accurate frequency clocks with very high precision are required
Mathematical Problems in Engineering considering nonstationary variations. It is based on the Wigner–Ville distribution [18, 19], proposed in 1932 for the characterization of quantum fluctuations. is time-frequency distribution is applicable for the analysis of nonstationary signals [20,21,22,23], radar signals [24, 25], biomedical signals [26,27,28], analysis of time-varying filters [29, 30], and image processing [31,32,33]
Differing from the power spectral density, which is a result of a time assimilation, assuming a stationary behavior within the temporal integration window, the Wigner–Ville distribution is a fundamental time-dependent measure, which can trend phase variations in ultrahigh resolution, depending on the sampling rate only
Summary
Due to the high data rates required to be transferred in communication networks, the demand for highaccuracy satellite navigation systems and the development of high-resolution radars, oscillators, and accurate frequency clocks with very high precision are required. Mathematical Problems in Engineering considering nonstationary variations It is based on the Wigner–Ville distribution [18, 19], proposed in 1932 for the characterization of quantum fluctuations. We introduce an analytic expression of the Wigner–Ville timefrequency distribution for the characterization of the temporal coherency of nonstationary signals produced by classical and quantum oscillators. Our proposed expression can reveal the time-varying frequencies generally seen in the clock error noise under nonstationary conditions and in other platforms such as oscillator under vibrations or shocks. E constants σ1, σ2, and σ3 are determined by the intensity of each of these respective noise components, resulting from internal electronic noise mechanisms in an oscillator, such as thermal (Johnson) noise, shot noise, and parametric noise, in which a near-dc process modulates the phase of the carrier [38]. E stochastic term (3) is the phase noise causing broadening in the line width
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