Abstract

Digital filters underpin the performance of coherent optical receivers which exploit digital signal processing (DSP) to mitigate transmission impairments. We outline the principles of such receivers and review our experimental investigations into compensation of polarization mode dispersion. We then consider the details of the digital filtering employed and present an analytical solution to the design of a chromatic dispersion compensating filter. Using the analytical solution an upper bound on the number of taps required to compensate chromatic dispersion is obtained, with simulation revealing an improved bound of 2.2 taps per 1000ps/nm for 10.7GBaud data. Finally the principles of digital polarization tracking are outlined and through simulation, it is demonstrated that 100krad/s polarization rotations could be tracked using DSP with a clock frequency of less than 500MHz.

© 2008 Optical Society of America

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References

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  1. P. S. Henry, "Lightwave Primer" IEEE J. Quantum Electron. 21, 1862-1879 (1985)
    [CrossRef]
  2. H. Bülow, "Electronic dispersion compensation," Proc. Opt. Fiber Comm. Conf. 2007, paper OMG5
  3. T. Okoshi and K. Kikuchi, "Coherent Optical Fiber Communications," KTK, 1988
  4. M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments" IEEE Photon. Technol. Lett. 16, 674 - 676 (2004).
    [CrossRef]
  5. S. Tsukamoto, D.-S Ly-Gagnon, K. Katoh, and K. Kikuchi, "Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission," in Proceedings of Optical Fiber Communications Conference 2005, paper PDP-29
  6. S. J. Savory, A. D. Stewart, S. Wood, G. Gavioli, M. G. Taylor, R. I. Killey, P. Bayvel, "Digital equalisation of 40Gbit/s per wavelength transmission over 2480km of standard fibre without optical dispersion compensation," in Proceedings of ECOC 2006, Cannes, France, paper Th2.5.5, Sep. 2006.
  7. C. R. S. Fludger, T. Duthel, T. Wuth, and C. Schulien, "Uncompensated transmission of 86Gbit/s polarization multiplexed RZ-QPSK over 100km of NDSF employing coherent equalisation," in Proceedings of ECOC 2006, Cannes, France, paper, Th4.3.3
  8. S. J. Savory, G. Gavioli, R. I. Killey and P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Express 15,2120-2126 (2007).
    [CrossRef] [PubMed]
  9. C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, "Wavelength Division Multiplexing (WDM) and Polarization Mode Dispersion (PMD) Performance of a Coherent 40Gbit/s Dual-Polarization Quadrature Phase Shift Keying (DP-QPSK) Transceiver," in Proceedings of Optical Fiber Communications Conference 2007, paper PDP16
  10. G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo "Efficient mitigation of fiber impairments in an ultra-long haul transmission of 40Gbit/s polarization-multiplexed data, by digital processing in a coherent receiver," in Proceedings of Optical Fiber Communications Conference 2007, paper PDP17
  11. C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E-D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, H. de Waardt, "10 x 111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK transmission over 2375 km employing coherent equalisation," in Proceedings of Optical Fiber Communications Conference 2007, paper PDP22
  12. G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19,969-971 (2007).
    [CrossRef]
  13. E. Ip and J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion" J. Lightwave Technol. 25,2033-2043 (2007)
    [CrossRef]
  14. D. van den Borne, H. de Waardt, G.-D. Khoe, T. Duthel, C. R. S. Fludger, C. Schulien, and E. -D. Schmidt, "Electrical PMD Compensation in 43-Gb/s POLMUX-NRZ-DQPSK enabled by Coherent Detection and Equalization," in Proceedings ECOC 2007, Berlin, Germany, invited paper 8.3.1
  15. S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvel, "Digital coherent receivers for uncompensated 42.8Gbit/s transmission over high PMD fibre," in Proceedings ECOC 2007, Berlin, Germany, invited paper 10.4.1
  16. A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
    [CrossRef]
  17. Q. Yu, L.-S. Yan, S. Lee, and A. E. Willner, "Loop-synchronous polarization scrambling for simulating polarization effects using recirculating fiber loops," J. Lightwave Technol. 21,1593-1600 (2003).
    [CrossRef]
  18. S. R. Desbruslais and P. R. Morkel, "Simulation of polarization mode dispersion and its effects in long-haul optically amplified lightwave systems," IEE Colloquium on International Transmission System, 6.1-6.6 (1994).
  19. M. J. D. Powell, Approximation Theory and Methods, Cambridge University Press, 1981.
  20. S. Haykin, "Signal processing: where physics and mathematics meet," IEEE Signal Process. Mag. 18,6-7 (2001)
    [CrossRef]
  21. G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, 2001), Chap. 3
  22. S. Betti, F. Curti, G. De Marchis, and E. Iannone, "A novel multilevel coherent optical system: four quadrature signaling," J. Lightwave Technol. 9,514-523 (1991)
    [CrossRef]
  23. Y. Han and G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Express 13,7527-7534 (2005).
    [CrossRef] [PubMed]
  24. D. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28,1867 - 1875 (1980).
    [CrossRef]
  25. C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
    [CrossRef]
  26. J.G. Proakis, Digital Communications, 4th Ed., (McGraw Hill, 2001).
  27. S. Haykin, Adaptive Filter Theory, 4th Ed., (Prentice Hall, 2001).
  28. J. J. Rodriguez-Andina, M. J. Moure and M. D. Valdes, "Features, design tools, and application domains of FPGAs," IEEE Trans Ind. Electron. 54,1810-1823 (2007).
    [CrossRef]
  29. T. Pfau,  et al., "PDL-tolerant real-time polarization-multiplexed QPSK transmission with digital coherent polarization diversity receiver" Proceedings of IEEE LEOS Summer Topical Meeting, 2007, paper MA3.3

2007

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19,969-971 (2007).
[CrossRef]

A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
[CrossRef]

J. J. Rodriguez-Andina, M. J. Moure and M. D. Valdes, "Features, design tools, and application domains of FPGAs," IEEE Trans Ind. Electron. 54,1810-1823 (2007).
[CrossRef]

S. J. Savory, G. Gavioli, R. I. Killey and P. Bayvel, "Electronic compensation of chromatic dispersion using a digital coherent receiver," Opt. Express 15,2120-2126 (2007).
[CrossRef] [PubMed]

E. Ip and J. M. Kahn, "Digital equalization of chromatic dispersion and polarization mode dispersion" J. Lightwave Technol. 25,2033-2043 (2007)
[CrossRef]

2005

2004

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments" IEEE Photon. Technol. Lett. 16, 674 - 676 (2004).
[CrossRef]

2003

2001

S. Haykin, "Signal processing: where physics and mathematics meet," IEEE Signal Process. Mag. 18,6-7 (2001)
[CrossRef]

1998

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

1991

S. Betti, F. Curti, G. De Marchis, and E. Iannone, "A novel multilevel coherent optical system: four quadrature signaling," J. Lightwave Technol. 9,514-523 (1991)
[CrossRef]

1985

P. S. Henry, "Lightwave Primer" IEEE J. Quantum Electron. 21, 1862-1879 (1985)
[CrossRef]

1980

D. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28,1867 - 1875 (1980).
[CrossRef]

Bayvel, P.

Behm, J. D.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Betti, S.

S. Betti, F. Curti, G. De Marchis, and E. Iannone, "A novel multilevel coherent optical system: four quadrature signaling," J. Lightwave Technol. 9,514-523 (1991)
[CrossRef]

Brown, D. R.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Casas, R.A.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Chen, Y.-K.

A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
[CrossRef]

Curti, F.

S. Betti, F. Curti, G. De Marchis, and E. Iannone, "A novel multilevel coherent optical system: four quadrature signaling," J. Lightwave Technol. 9,514-523 (1991)
[CrossRef]

De Marchis, G.

S. Betti, F. Curti, G. De Marchis, and E. Iannone, "A novel multilevel coherent optical system: four quadrature signaling," J. Lightwave Technol. 9,514-523 (1991)
[CrossRef]

Endres, T. J.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Gavioli, G.

Godard, D.

D. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28,1867 - 1875 (1980).
[CrossRef]

Goldfarb, G.

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19,969-971 (2007).
[CrossRef]

Han, Y.

Haykin, S.

S. Haykin, "Signal processing: where physics and mathematics meet," IEEE Signal Process. Mag. 18,6-7 (2001)
[CrossRef]

Henry, P. S.

P. S. Henry, "Lightwave Primer" IEEE J. Quantum Electron. 21, 1862-1879 (1985)
[CrossRef]

Iannone, E.

S. Betti, F. Curti, G. De Marchis, and E. Iannone, "A novel multilevel coherent optical system: four quadrature signaling," J. Lightwave Technol. 9,514-523 (1991)
[CrossRef]

Ip, E.

Johnson, C. R.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Kahn, J. M.

Kaneda, N.

A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
[CrossRef]

Killey, R. I.

Koc, U-V

A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
[CrossRef]

Lee, S.

Leven, A.

A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
[CrossRef]

Li, G.

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19,969-971 (2007).
[CrossRef]

Y. Han and G. Li, "Coherent optical communication using polarization multiple-input-multiple-output," Opt. Express 13,7527-7534 (2005).
[CrossRef] [PubMed]

Moure, M. J.

J. J. Rodriguez-Andina, M. J. Moure and M. D. Valdes, "Features, design tools, and application domains of FPGAs," IEEE Trans Ind. Electron. 54,1810-1823 (2007).
[CrossRef]

Rodriguez-Andina, J. J.

J. J. Rodriguez-Andina, M. J. Moure and M. D. Valdes, "Features, design tools, and application domains of FPGAs," IEEE Trans Ind. Electron. 54,1810-1823 (2007).
[CrossRef]

Savory, S. J.

Schniter, P.

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Taylor, M. G.

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments" IEEE Photon. Technol. Lett. 16, 674 - 676 (2004).
[CrossRef]

Valdes, M. D.

J. J. Rodriguez-Andina, M. J. Moure and M. D. Valdes, "Features, design tools, and application domains of FPGAs," IEEE Trans Ind. Electron. 54,1810-1823 (2007).
[CrossRef]

Willner, A. E.

Yan, L.-S.

Yu, Q.

IEEE J. Quantum Electron.

P. S. Henry, "Lightwave Primer" IEEE J. Quantum Electron. 21, 1862-1879 (1985)
[CrossRef]

IEEE Photon. Technol. Lett.

M. G. Taylor, "Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments" IEEE Photon. Technol. Lett. 16, 674 - 676 (2004).
[CrossRef]

G. Goldfarb and G. Li, "Chromatic dispersion compensation using digital IIR filtering with coherent detection," IEEE Photon. Technol. Lett. 19,969-971 (2007).
[CrossRef]

A. Leven, N. Kaneda, U-V Koc, and Y.-K. Chen "Frequency Estimation in Intradyne Reception," IEEE Photon. Technol. Lett. 19,366 - 368 (2007)
[CrossRef]

IEEE Signal Process. Mag.

S. Haykin, "Signal processing: where physics and mathematics meet," IEEE Signal Process. Mag. 18,6-7 (2001)
[CrossRef]

IEEE Trans Ind. Electron.

J. J. Rodriguez-Andina, M. J. Moure and M. D. Valdes, "Features, design tools, and application domains of FPGAs," IEEE Trans Ind. Electron. 54,1810-1823 (2007).
[CrossRef]

IEEE Trans. Commun.

D. Godard, "Self-recovering equalization and carrier tracking in two-dimensional data communication systems," IEEE Trans. Commun. 28,1867 - 1875 (1980).
[CrossRef]

J. Lightwave Technol.

Opt. Express

Proc. IEEE

C. R. Johnson, P. Schniter, T. J. Endres, J. D. Behm, D. R. Brown, R.A. Casas, "Blind equalization using the Constant Modulus Criterion: A review," Proc. IEEE 86,1927-1950 (1998).
[CrossRef]

Other

J.G. Proakis, Digital Communications, 4th Ed., (McGraw Hill, 2001).

S. Haykin, Adaptive Filter Theory, 4th Ed., (Prentice Hall, 2001).

G. P. Agrawal, Nonlinear Fiber Optics, (Academic Press, 2001), Chap. 3

H. Bülow, "Electronic dispersion compensation," Proc. Opt. Fiber Comm. Conf. 2007, paper OMG5

T. Okoshi and K. Kikuchi, "Coherent Optical Fiber Communications," KTK, 1988

T. Pfau,  et al., "PDL-tolerant real-time polarization-multiplexed QPSK transmission with digital coherent polarization diversity receiver" Proceedings of IEEE LEOS Summer Topical Meeting, 2007, paper MA3.3

C. Laperle, B. Villeneuve, Z. Zhang, D. McGhan, H. Sun, and M. O’Sullivan, "Wavelength Division Multiplexing (WDM) and Polarization Mode Dispersion (PMD) Performance of a Coherent 40Gbit/s Dual-Polarization Quadrature Phase Shift Keying (DP-QPSK) Transceiver," in Proceedings of Optical Fiber Communications Conference 2007, paper PDP16

G. Charlet, J. Renaudier, M. Salsi, H. Mardoyan, P. Tran, and S. Bigo "Efficient mitigation of fiber impairments in an ultra-long haul transmission of 40Gbit/s polarization-multiplexed data, by digital processing in a coherent receiver," in Proceedings of Optical Fiber Communications Conference 2007, paper PDP17

C. R. S. Fludger, T. Duthel, D. van den Borne, C. Schulien, E-D. Schmidt, T. Wuth, E. de Man, G. D. Khoe, H. de Waardt, "10 x 111 Gbit/s, 50 GHz Spaced, POLMUX-RZ-DQPSK transmission over 2375 km employing coherent equalisation," in Proceedings of Optical Fiber Communications Conference 2007, paper PDP22

S. Tsukamoto, D.-S Ly-Gagnon, K. Katoh, and K. Kikuchi, "Coherent demodulation of 40-Gbit/s polarization-multiplexed QPSK signals with 16-GHz spacing after 200-km transmission," in Proceedings of Optical Fiber Communications Conference 2005, paper PDP-29

S. J. Savory, A. D. Stewart, S. Wood, G. Gavioli, M. G. Taylor, R. I. Killey, P. Bayvel, "Digital equalisation of 40Gbit/s per wavelength transmission over 2480km of standard fibre without optical dispersion compensation," in Proceedings of ECOC 2006, Cannes, France, paper Th2.5.5, Sep. 2006.

C. R. S. Fludger, T. Duthel, T. Wuth, and C. Schulien, "Uncompensated transmission of 86Gbit/s polarization multiplexed RZ-QPSK over 100km of NDSF employing coherent equalisation," in Proceedings of ECOC 2006, Cannes, France, paper, Th4.3.3

D. van den Borne, H. de Waardt, G.-D. Khoe, T. Duthel, C. R. S. Fludger, C. Schulien, and E. -D. Schmidt, "Electrical PMD Compensation in 43-Gb/s POLMUX-NRZ-DQPSK enabled by Coherent Detection and Equalization," in Proceedings ECOC 2007, Berlin, Germany, invited paper 8.3.1

S. J. Savory, V. Mikhailov, R. I. Killey, and P. Bayvel, "Digital coherent receivers for uncompensated 42.8Gbit/s transmission over high PMD fibre," in Proceedings ECOC 2007, Berlin, Germany, invited paper 10.4.1

S. R. Desbruslais and P. R. Morkel, "Simulation of polarization mode dispersion and its effects in long-haul optically amplified lightwave systems," IEE Colloquium on International Transmission System, 6.1-6.6 (1994).

M. J. D. Powell, Approximation Theory and Methods, Cambridge University Press, 1981.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic of a phase and polarization diverse receiver where Ex , Ey and Elo are the electric fields associated with the horizontal and vertical polarization components of the input optical signal and local oscillator respectively

Fig. 2.
Fig. 2.

Schematic of the DSP blocks in a digital coherent receiver

Fig. 3.
Fig. 3.

Functionality of the digital filtering stage. For linear filtering the order of the two sub-blocks may of course be reversed

Fig. 4.
Fig. 4.

Experimental setup of the recirculating loop experiment full details of which are given in [15]. Recovered constellations are obtained with 100ps mean DGD (32ps/loop) and 53,712ps/nm chromatic dispersion from 3200km fibe

Fig 5.
Fig 5.

The impact of PMD on the performance (left), and the pdf of the BER (right)

Fig. 6.
Fig. 6.

BER as a function of OSNR for 0km, 4000km (251 taps) and 40000km (2501 taps)

Fig. 7.
Fig. 7.

Performance with OSNR=9.5dB of Q=√2erfcinv(2BER) versus normalized number of taps being the ratio of the number of taps to the maximal truncation window given by Eq. (9)

Fig. 8.
Fig. 8.

Frequency response of Q using the constant modulus algorithm (red), and the decision directed least mean squares algorithm (blue) for several values of convergence parameter with 3 taps in each MIMO filter

Fig. 9.
Fig. 9.

Frequency response of Q using the constant modulus algorithm (red), and the decision directed least mean squares algorithm (blue) for several values of convergence parameter with 13 taps in each MIMO filter

Fig. 10.
Fig. 10.

Impact the update rate on a MIMO equalizer with 13 taps

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

( i 1 i 2 i 3 i 4 )= 2 5 ( Re( E x E lo * ) Im( E x E lo * ) Re( E y E lo * ) Im( E y E lo * ) ) coherent terms + 1 10 ( 2| E x | 2 +2| E lo | 2 4| E x | 2 +| E lo | 2 2| E y | 2 +2| E lo | 2 4| E y | 2 +| E lo | 2 ) direct detection terms
DGD = DGD per loop × 8 3 π × number of recirculations
A ( z , t ) z = j D λ 2 4 πc 2 A ( z , t ) t 2
G ( z , ω ) = exp ( j D λ 2 4 πc ω 2 )
g ( z , t ) = c j D λ 2 z exp ( j πc D λ 2 z t 2 )
g c ( z , t ) = jc D λ 2 z exp ( j ϕ ( t ) ) where ϕ ( t ) = πc D λ 2 z t 2
ω = ϕ ( t ) t = 2 πc D λ 2 z t
D λ 2 z 2 cT t D λ 2 z 2 cT
a k = jc T 2 D λ 2 z exp ( j πc T 2 D λ 2 z k 2 ) N 2 k N 2 and N = 2 × D λ 2 z 2 c T 2 + 1
x out ( k ) = h xx T · x p + h xy T · y p = m = 0 M 1 h xx ( m ) x p ( k m ) + h xy ( m ) y p ( k m )
d ε x 2 d h xx = 0 ; d ε x 2 d h xy = 0 ; d ε y 2 d h yx = 0 ; d ε y 2 d h yy = 0
h xx h xx μ 4 d ε x 2 d h xx = h xx + μ ε x x out · x ̅ p
h xy h xy μ 4 d ε x 2 d h xy = h xy + μ ε x x out · y p
h yx h yx μ 4 d ε y 2 d h yx = h yx + μ ε y y out · x p
h yy h yy μ 4 d ε y 2 d h yy = h yy + μ ε y y out · y p
h xx h xx μ 2 d ε x 2 d h xx = h xx + μ ε x ·   x p
h xy h xy μ 2 d ε x 2 d h xy = h xy + μ ε x · y p
h yx h yx μ 2 d ε y 2 d h yx = h yx + μ ε y · x p
h yy h yy μ 2 d ε y 2 d h yy = h yy + μ ε y   · y p
J = ( cos ωt sin ωt sin ωt cos ωt )

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