![](bg4.png)
2014; Yakovleva, 2014; Yakovleva, 2015) allow an
accurate estimating of both the signal
and noise (
) parameters based
upon the sampled measurements. In other words, by
means of calculating the initial, undistorted values of
the three signals’ amplitudes we would “freeze” the
picture as a noise-free one and thus calculate the
needed phase difference value just on the basis of
geometrical considerations by the formula:
222
3 1 2
12
arccos
2
AAA
AA
Below some results of the numerical simulation of
the proposed technique are presented. Table 1
demonstrates the dependence of the absolute error
modulus
at calculating the
sought for signal’s phase shift upon a number of
parameters such as the sample length, the signal-to-
noise ratio, etc. The denotations are as follows:
- the phase shift calculated according to the
above algorithm,
- the real phase shift (at the
numerical experiment illustrated by Table 1 the
value of the real phase shift was equal to 1,318),
- the value that
characterizes the signal-to-noise ratio,
- the
number of measurements in a sample.
Table 1 presents the results of the technique’s
numerical simulation, i.e. the calculated values of
the absolute error modulus are provided, at
averaging by
measurements.
Table 1: Numerically calculated magnitude of the absolute
error modulus
as dependent on the
signal-to-noise ratio
and the sample length.
.
4 CONCLUSIONS
The paper presents an original technique of
measuring the phase difference between two quasi-
harmonic optical signals based upon the statistical
processing of the amplitudes values of the following
three signals: the two compared signals and their
sum. The theoretical consideration of the problem is
provided. The amplitudes of the three signals to be
analyzed are shown to obey the Rice statistical
distribution. The algorithm of the proposed
technique implementation consists in the joint
reconstruction of the undistorted signals’ amplitudes
against the noise background. Therefore the sough
for phase shift is obtained as a result of the
amplitude measurements only what significantly
decreases the demands to the equipment and
simplifies the realization of the proposed method in
a wide circle of applied tasks to be solved in
numerous ranging and communication systems. The
digital experiments confirm the theoretical
conclusions on the feasibility and efficiency of the
proposed technique.
The work was funded by RFBR according to the
research project № 17-07-00064.
REFERENCES
Kinkulkin, I. E., Rubtsov, V. D., Fabrik, M. A. 1979. The
Phase Method of Coordinates’ Determination,
Moscow. Sov. Radio, 160p.
Chmykh, M. K. 1993. Digital Phase Meter, Moscow, Radio
i svyaz', 184p.
Smirnov, V. N., Kucherov, M. V. 2004. Broadband digital
phasemeter, Voprosy radioelektroniki, vol.1, pp. 33-
41.
Webster, J. G. (Ed.), 2004. Electrical Measurement,
Signal Processing, and Displays, Boca Raton: CRC
Press, 320p.
Mahmud, S. M. 1989. Error analysis of digital phase
measurement of distorted waves, IEEE Trans. on
Instrumentation and Measurement, vol. 38, N 1, pp. 6-
9.
Liang, Y. R., Duan, H. Z., Yeh, H. C., Luo, J. 2012.
Fundamental limits on the digital phase measurement
method based on cross-correlation analysis, Rev. Sci.
Instrum., vol. 83, N 9, 095119.
Mahmud, S. M. 1990. High precision phase measurement
using reduced sine and cosine tables, IEEE Trans. on
Instrumentation and Measurement, vol. 39, N 1, pp.
56-50.
Mahmud, S. M. 1989. High precision phase measurement
using adaptive sampling, IEEE Trans. on
Instrumentation and Measurement, vol. 38, N 5, pp.
954–960.
Sedlacek, M., Krumpholc, M. 2005. Digital measurement
of phase difference - a comparative study DSP
algorithms, Metrology and Measurement Systems, vol.
XII, N 4, pp. 427–449.
Ignat'ev, V. K., Nikitin, A.V., Yushanov, S.V. 2010.
Parametric analysis of oscillations with slowly varying
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