Determining the phase shift of quasiharmonic signals through envelope analysis
Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia
Full text of article: Russian language.
The paper presents a new technique for the accurate measurement of the phase difference between two quasi-harmonic optical signals through analyzing and processing their envelope values obeying the Rice statistical distribution. With this technique, the envelope values of three signals are measured: two initial quasi-harmonic signals for which the phase difference is measured and a third signal formed as superposition of the first two. The phase shift under measurement is calculated from simple geometrical considerations as the angle of a triangle formed by the amplitude values of the reconstructed undistorted signals. The fundamental distinction of the proposed technique consists in the fact that the phase characteristics are derived from the amplitude measurements alone, thus significantly mitigating the requirements imposed on the equipment and simplifying the practical implementation of the method. It is proposed that the undistorted amplitudes should be estimated using methods of the Rician data analysis. The paper provides a strict mathematical analysis of the problem and computer simulation results. The ability to conduct accurate phase shift measurements based on the proposed method is useful for a wide range of applied tasks solved in numerous ranging and communication systems.
phase shift measurement, Rice distribution, signal sampling, quasiharmonic signal method of moments.
Yakovleva TV. Determining the phase shift of quasiharmonic signals through envelope analysis. Computer Optics 2017; 41(6): 950-956. DOI: 10.18287/2412-6179-2017-41-6-950-956.
- Kinkulkin IE, Rubtsov VD, Fabrik MA. The phase method of coordinates’ determination [In Russian]. Moscow: "Sovetskoe Radio" Publisher; 1979.
- Chmykh MK. Digital phaseometry [In Russian]. Moscow: "Radio i svyaz" Publisher; 1993. ISBN: 5-256-01043-3.
- Smirnov VN, Kucherov MV. Broadband digital phase meter [In Russian]. Voprosy radioelektroniki 2004; 1(1): 33-41.
- Webster JG, ed. Electrical measurement, signal processing, and displays. Boca Raton: CRC Press; 2004. ISBN: 0-8493-1733-9.
- Mahmud SM. Error analysis of digital phase measurement of distorted waves. IEEE Transactions on Instrumentation and Measurement 1989; 38(1): 6-9. DOI: 10.1109/19.19989.
- Liang YR, Duan HZ, Yeh HC, Luo J. Fundamental limits on the digital phase measurement method based on cross-correlation analysis. Rev Sci Instrum 2012; 83(9): 095119.
- Mahmud SM. High precision phase measurement using reduced sine and cosine tables. IEEE Transactions on Instrumentation and Measurement1990; 39(1): 56-50. DOI: 10.1109/19.50416.
- Mahmud SM. High precision phase measurement using adaptive sampling. IEEE Transactions on Instrumentation and Measurement1989;38(5): 954-960. DOI: 10.1109/19.39036.
- Sedlacek M, Krumpholc M. Digital measurement of phase difference – a comparative study DSP algorithms. Metrology and Measurement System 2005; 12(4): 427-449.
- Ignat'ev VK, Nikitin AV, Yushanov SV. Parametric analysis of oscillations with slowly varying frequency. Radiophysics and Quantum Electronics 2010; 53(2): 132-145.
- Ignat'ev VK, Nikitin AV, Yushanov SV. Measurement of the quasi-harmonic signals’ phase shift. Numerical Methods and Programming 2013; 14: 424-431.
- Ramos PM, Serra AC. A new sine-?tting algorithm for accurate amplitude and phase measurements in two channel acquisition systems. Measurement 2008; 41(2): 135-143. DOI: 10.1016/j.measurement.2006.03.011.
- Hing ChS, Zhenhua Zh. Two accurate phase-difference estimators for dual-channel sine-wave model. EURASIP Journal on Advances in Signal Processing 2013; 2013: 122. DOI: 10.1186/1687-6180-2013-122.
- Rytov SM. Introduction into statistical radio-physics. Pt 1. Random Processes [In Russian]. Moscow: "Nauka" Publisher; 1976.
- Abramowitz M, Stegun IA, eds. Handbook of mathematical functions: With formulas, graphs and mathematical tables. Washington D.C.: National Bureau of Standards; 1964.
- Yakovleva TV, Kulberg NS. Noise and signal estimation in MRI: two-parametric analysis of rice-distributed data by means of the maximum likelihood approach. American Journal of Theoretical and Applied Statistics 2013; 2(3): 67-79. DOI: 10.11648/j.ajtas.20130203.15.
- Yakovleva TV, Kulberg NS. Methods of mathematical statistics in two-parameter analysis of Rician signals. Doklady Mathematics 2014; 90(3): 675-679. DOI: 10.1134/S1064562414070060.
- Yakovleva TV. Review of MRI processing techniques and elaboration of a new two-parametric method of moments [In Russian]. Computer Research and Modeling 2014; 6(2): 231-244.
- Yakovleva TV. A theory of signal processing at the Rice distribution. Moscow: Dorodnicyn Computing Centre of RAS; 2015.
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