Apparatus for using a time interval counter to measure frequency stability

An apparatus for measuring the relative stability of two signals is disclosed comprising a means for mixing the two signals down to a beat note sine wave and for producing a beat note square wave whose upcrossings are the same as the sine wave. A source of reference frequency is supplied to a clock divider and interval counter to synchronize them and to generate a picket fence for providing a time reference grid of period shorter than the beat period. An interval counter is employed to make a preliminary measurement between successive upcrossings of the beat note square wave for providing an approximate time interval therebetween as a reference. The beat note square wave and the picket fence are then provided to the interval counter to provide an output consisting of the time difference between the upcrossing of each beat note square wave cycle and the next picket fence pulse such that the counter is ready for each upcrossing and dead time is avoided. A computer containing an algorithm for calculating the exact times of the beat note upcrossings then computes the upcrossing times

Frequency stability review

Certain aspects of the description and measurement of oscillator stability are treated. Topics covered are time and frequency deviations, Allan variance, the zero-crossing counter measurement technique, frequency drift removal, and the three-cornered hat

The fundamental structure function of oscillator noise models

Continuous-time models of oscillator phase noise x(t) usually have stationary nth differences, for some n. The covariance structure of such a model can be characterized in the time domain by the structure function: D sub n (t;gamma sub 1, gamma sub 2) = E delta (n) sub gamma sub 1 x(s+t) delta(n) sub gamma sub 2 x (s). Although formulas for the special case D sub 2 (0;gamma,gamma) (the Allan variance times 2 gamma(2)) exist for power-law spectral models, certain estimation problems require a more complete knowledge of (0). Exhibited is a much simpler function of one time variable, D(t), from which (0) can easily be obtained from the spectral density by uncomplicated integrations. Believing that D(t) is the simplest function of time that holds the same information as (0), D(t) is called the fundamental structure function. D(t) is computed for several power-law spectral models. Two examples are D(t) = K/t/(3) for random walk FM, D(t) = Kt(2) 1n/t/ for flicker FM. Then, to demonstrate its use, a BASIC program is given that computes means and variances of two Allan variance estimators, one of which incorporates a method of frequency drift estimation and removal

Orthogonal sets of data windows constructed from trigonometric polynomials

Suboptimal, easily computable substitutes for the discrete prolate-spheroidal windows used by Thomson for spectral estimation are given. Trigonometric coefficients and energy leakages of the window polynomials are tabulated

A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. A theorem which obtains the structure function (covariance of the nth differences) of such a process in terms of the differences of a single function of one time variable is proven. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability

Open-loop radio science with a suppressed-carrier signal

When a suppressed-carrier signal is squared, the carrier reappears in doubled form. An open-loop receiver can be used to deliver a recording of a band-limited waveform containing this carrier, whose amplitude and phase can be tracked by the radio science experimenter

A compact presentation of DSN array telemetry performance

The telemetry performance of an arrayed receiver system, including radio losses, is often given by a family of curves giving bit error rate vs bit SNR, with tracking loop SNR at one receiver held constant along each curve. This study shows how to process this information into a more compact, useful format in which the minimal total signal power and optimal carrier suppression, for a given fixed bit error rate, are plotted vs data rate. Examples for baseband-only combining are given. When appropriate dimensionless variables are used for plotting, receiver arrays with different numbers of antennas and different threshold tracking loop bandwidths look much alike, and a universal curve for optimal carrier suppression emerges

Digital signal processing in the radio science stability analyzer

The Telecommunications Division has built a stability analyzer for testing Deep Space Network installations during flight radio science experiments. The low-frequency part of the analyzer operates by digitizing wave signals with bandwidths between 80 Hz and 45 kHz. Processed outputs include spectra of signal, phase, amplitude, and differential phase; time series of the same quantities; and Allan deviation of phase and differential phase. This article documents the digital signal-processing methods programmed into the analyzer

Exact numerical simulation of power-law noises

Many simulations of stochastic processes require colored noises: I describe here an exact numerical method to simulate power-law noises: the method can be extended to more general colored noises, and is exact for all time steps, even when they are unevenly spaced (as may often happen for astronomical data, see e.g. N. R. Lomb, Astrophys. Space Sci. {\bf 39}, 447 (1976)). The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity.Comment: 14 postscript figures, accepted for publication on Phys. Rev.

The Deep Space Network stability analyzer

A stability analyzer for testing NASA Deep Space Network installations during flight radio science experiments is described. The stability analyzer provides realtime measurements of signal properties of general experimental interest: power, phase, and amplitude spectra; Allan deviation; and time series of amplitude, phase shift, and differential phase shift. Input ports are provided for up to four 100 MHz frequency standards and eight baseband analog (greater than 100 kHz bandwidth) signals. Test results indicate the following upper bounds to noise floors when operating on 100 MHz signals: -145 dBc/Hz for phase noise spectrum further than 200 Hz from carrier, 2.5 x 10(exp -15) (tau =1 second) and 1.5 x 10(exp -17) (tau =1000 seconds) for Allan deviation, and 1 x 10(exp -4) degrees for 1-second averages of phase deviation. Four copies of the stability analyzer have been produced, plus one transportable unit for use at non-NASA observatories