The data we look at here is the measured time difference of two Hydrogen maser clocks whose output are steered towards UTC. This system would be generically classified as a "driven" system since we are not looking at two free running clocks. In time and frequency keeping most of the "signals" are described as "noise". This will be a first look at a good system with an attempt at isolation of any chaotic signal(s) within. We start with figure 1 which is the time series. These are simple one day averages of nonimnally sampled hour TWSTT experiments. The basic statistics of the data are as indicated below.

N 1194 (days)

Mean 0.174 (Nanoseconds)

Minimum -1.94

Maximum 2.49

Variance 0.478

Std. Deviation 0.691

Skewness 0.276

Kurtosis 0.616

Figure 1 The original TWSTT signal.

Next we generate the power spectra using the method given in reference 1. The time and frequency communiity most often plots the power spectra as log/log plots which makes it easy to detection power law components of the "noise". Iniitially the spectra is flat and later shows a slope change. This might indicate a low-order attractor which often show broadband peaks in power spectra, i.e. there are no sharp peaks indicative of linear periodic signals.

Figure 2 The Fourier spectrum of the TWSTT signal.

Next is shown the standard autocorrelation function. The first minimum is located at a lag of 16, but a deeper first minimum is located at a lag of 32.

Figure 3 The autocorrelation function of the TWSTT signal.

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Figure 4 The global average mutual information of the TWSTT signal.

Figure 5 The global false nearest neighbors of the TWSTT signal.

Figure 6 The correlation dimension of the TWSTT signal.

Figure 7 The unfolded attactor consisting of the "quantum noise" of the time
transfer and clocks involved.

Figure 8 shows the VRA plot of the TWSTT signal with dimension of 1 and a time
lag of 1. The STE is 83%. All VRA plots were produced using the software
in reference 1. (gif - 125 kb)

Figure 9 shows the VRA plot of the TWSTT signal with dimension of 2 and a time
lag of 8. The STE is 80%. (gif - 131 kb)

Figure 10 shows the VRA plot of the TWSTT signal with dimension of 8 and a time
lag of 8. The STE is 80%. (gif - 121 kb)

Figure 11 shows the VRA plot of the TWSTT signal with dimension of 15 and a time
lag of 15. The STE is 80%. (gif - 120 kb)

Figure 12 shows the VRA plot of the TWSTT signal with dimension of 30 and a time
lag of 30. There is not enough data to compute the STE. (gif - 101 kb)

Figure 13 shows the VRA plot of the TWSTT signal with dimension of 31 and a time
lag of 31. There is not enough data to compute the STE. (gif - 97 kb)

Figure 14 shows the VRA plot of the TWSTT signal with dimension of 32 and a time
lag of 32. There is not enough data to compute the STE. (gif - 88 kb)

- J. A. Barnes, 1993, "A Digital Equivalent of an Analog Spectrum Analyzer,"
Proceedings of the 1993 IEEE International Frequency Control Symposium, 2-4
June 1993, Salt Lake City, Utah, USA, p. 270-281.

- Kononov, Eugene, (October 1, 1999), Visual Recurrence Analyis, Software
Version 4.0.

- Applied Nonlinear Sciences, 1997, Contemporary Signal Processing for
Windows, cspW, Software Version 1.2.

- Schroeder, Manfred, 1991, "Fractals, Chaos, Power Laws: Minutes from an
Infinite Paradise", W. H. Freeman Company, New York, pp. 429.

- Gutzwiller, Martin C., 1990, Chaos in Classical and Quantum Mechanics,
(Interdisciplinary Applied Mathematics Volume 1), Springer-Verlag, New York,
pp. 432.