Abstract

Using a simplified chirp z-transform (CZT) algorithm based on the discrete-time convolution method, this paper presents the synthesis of a simplified architecture of a reconfigurable optical chirp z-transform (OCZT) processor based on the silica-based planar lightwave circuit (PLC) technology. In the simplified architecture of the reconfigurable OCZT, the required number of optical components is small and there are no waveguide crossings which make fabrication easy. The design of a novel type of optical discrete Fourier transform (ODFT) processor as a special case of the synthesized OCZT is then presented to demonstrate its effectiveness. The designed ODFT can be potentially used as an optical demultiplexer at the receiver of an optical fiber orthogonal frequency division multiplexing (OFDM) transmission system.

© 2014 Optical Society of America

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References

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    [Crossref]
  7. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
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2014 (1)

2011 (1)

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

2010 (3)

K. Takiguchi, M. Oguma, H. Takahashi, and A. Mori, “Integrated-optic eight-channel OFDM demultiplexer and its demonstration with 160 Gbit/s signal reception,” Electron. Lett. 46(8), 575–576 (2010).
[Crossref]

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

2006 (2)

K. Takiguchi, M. Itoh, and T. Shibata, “Optical-signal-processing device based on waveguide-type variable delay lines and optical gates,” J. Lightwave Technol. 24(7), 2593–2601 (2006).
[Crossref]

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

1996 (1)

N. Q. Ngo, L. N. Binh, and X. Dai, “Optical dark-soliton generators and detectors,” Opt. Comms. 132(3−4), 389–402 (1996).
[Crossref]

1969 (2)

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm,” IEEE Trans. Audio Electroacoust. 17(2), 86–92 (1969).
[Crossref]

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm and its application,” Bell Syst. Tech. J. 48(5), 1249–1292 (1969).
[Crossref]

Baets, R.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Bassi, P.

Becker, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Binh, L. N.

N. Q. Ngo, L. N. Binh, and X. Dai, “Optical dark-soliton generators and detectors,” Opt. Comms. 132(3−4), 389–402 (1996).
[Crossref]

Bogaerts, W.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Bonk, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Brouckaert, J.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Dai, X.

N. Q. Ngo, L. N. Binh, and X. Dai, “Optical dark-soliton generators and detectors,” Opt. Comms. 132(3−4), 389–402 (1996).
[Crossref]

De Vos, K.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Dreschmann, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Dumon, P.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Ellermeyer, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Freude, W.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Frey, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Hashimoto, T.

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

Hida, Y.

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

Hillerkuss, D.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Huber, G.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Huebner, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Itoh, M.

Jordan, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Kleinow, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Koenig, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Koos, C.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Leuthold, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Li, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Ludwig, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Lutz, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Marculescu, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Melloni, A.

Meyer, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Moeller, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Mori, A.

K. Takiguchi, M. Oguma, H. Takahashi, and A. Mori, “Integrated-optic eight-channel OFDM demultiplexer and its demonstration with 160 Gbit/s signal reception,” Electron. Lett. 46(8), 575–576 (2010).
[Crossref]

Morichetti, F.

Narkiss, N.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Nebendahl, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Ngo, N. Q.

N. Q. Ngo, L. N. Binh, and X. Dai, “Optical dark-soliton generators and detectors,” Opt. Comms. 132(3−4), 389–402 (1996).
[Crossref]

Oehler, A.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Oguma, M.

K. Takiguchi, M. Oguma, H. Takahashi, and A. Mori, “Integrated-optic eight-channel OFDM demultiplexer and its demonstration with 160 Gbit/s signal reception,” Electron. Lett. 46(8), 575–576 (2010).
[Crossref]

Orlandi, P.

Parmigiani, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Petropoulos, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Rabiner, L. R.

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm,” IEEE Trans. Audio Electroacoust. 17(2), 86–92 (1969).
[Crossref]

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm and its application,” Bell Syst. Tech. J. 48(5), 1249–1292 (1969).
[Crossref]

Rader, C. M.

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm,” IEEE Trans. Audio Electroacoust. 17(2), 86–92 (1969).
[Crossref]

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm and its application,” Bell Syst. Tech. J. 48(5), 1249–1292 (1969).
[Crossref]

Resan, B.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Roeger, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Saida, T.

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

Sakamaki, Y.

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

Schafer, R. W.

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm and its application,” Bell Syst. Tech. J. 48(5), 1249–1292 (1969).
[Crossref]

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm,” IEEE Trans. Audio Electroacoust. 17(2), 86–92 (1969).
[Crossref]

Schellinger, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Schmogrow, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Selvaraja, S. K.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Shibata, T.

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

K. Takiguchi, M. Itoh, and T. Shibata, “Optical-signal-processing device based on waveguide-type variable delay lines and optical gates,” J. Lightwave Technol. 24(7), 2593–2601 (2006).
[Crossref]

Sigurdsson, G.

Sorel, M.

Strain, M. J.

Takahashi, H.

K. Takiguchi, M. Oguma, H. Takahashi, and A. Mori, “Integrated-optic eight-channel OFDM demultiplexer and its demonstration with 160 Gbit/s signal reception,” Electron. Lett. 46(8), 575–576 (2010).
[Crossref]

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

Takiguchi, K.

K. Takiguchi, M. Oguma, H. Takahashi, and A. Mori, “Integrated-optic eight-channel OFDM demultiplexer and its demonstration with 160 Gbit/s signal reception,” Electron. Lett. 46(8), 575–576 (2010).
[Crossref]

K. Takiguchi, M. Itoh, and T. Shibata, “Optical-signal-processing device based on waveguide-type variable delay lines and optical gates,” J. Lightwave Technol. 24(7), 2593–2601 (2006).
[Crossref]

Tamura, M.

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

Teschke, M.

Vallaitis, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Van Thourhout, D.

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

Weingarten, K.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Winter, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

D. Hillerkuss, M. Winter, M. Teschke, A. Marculescu, J. Li, G. Sigurdsson, K. Worms, S. Ben Ezra, N. Narkiss, W. Freude, and J. Leuthold, “Simple all-optical FFT scheme enabling Tbit/s real-time signal processing,” Opt. Express 18(9), 9324–9340 (2010).
[Crossref] [PubMed]

Worms, K.

Bell Syst. Tech. J. (1)

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm and its application,” Bell Syst. Tech. J. 48(5), 1249–1292 (1969).
[Crossref]

Electron. Lett. (1)

K. Takiguchi, M. Oguma, H. Takahashi, and A. Mori, “Integrated-optic eight-channel OFDM demultiplexer and its demonstration with 160 Gbit/s signal reception,” Electron. Lett. 46(8), 575–576 (2010).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (1)

W. Bogaerts, S. K. Selvaraja, P. Dumon, J. Brouckaert, K. De Vos, D. Van Thourhout, and R. Baets, “Silicon-on-insulator spectral filters fabricated with CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 16(1), 33–44 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Y. Sakamaki, T. Saida, T. Shibata, Y. Hida, T. Hashimoto, M. Tamura, and H. Takahashi, “Y-branch waveguides with stabilized splitting ratio designed by wavefront matching method,” IEEE Photon. Technol. Lett. 18(7), 817–819 (2006).
[Crossref]

IEEE Trans. Audio Electroacoust. (1)

L. R. Rabiner, R. W. Schafer, and C. M. Rader, “The chirp z-transform algorithm,” IEEE Trans. Audio Electroacoust. 17(2), 86–92 (1969).
[Crossref]

J. Lightwave Technol. (2)

Nat. Photonics (1)

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbits−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011).
[Crossref]

Opt. Comms. (1)

N. Q. Ngo, L. N. Binh, and X. Dai, “Optical dark-soliton generators and detectors,” Opt. Comms. 132(3−4), 389–402 (1996).
[Crossref]

Opt. Express (1)

Other (5)

K. Takiguchi, T. Kitoh, M. Oguma, Y. Hashizume, and H. Takahashi, “Integrated-optic OFDM demultiplexer using multi-mode interference coupler-based optical DFT circuit,” Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference, OSA Technical Digest (Optical Society of America, 2012), paper OM3J.6.
[Crossref]

N. Q. Ngo, “Optical chirp z-transform processor − part I: design,” J. Lightwave Technol. submitted for publication.

N. Q. Ngo, “Optical chirp z-transform processor − part II: application,” J. Lightwave Technol. submitted for publication.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, and Applications (third edition, Prentice Hall, 1996), pp. 152 and pp. 482−483.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing (Prentice Hall, 1989), pp. 623−628.

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Figures (3)

Fig. 1
Fig. 1 Block diagram representation of the simplified CZT algorithm using the discrete-time convolution method.
Fig. 2
Fig. 2 Schematic diagram of the synthesized reconfigurable OCZT processor using the silica-based PLC technology. TC: tunable coupler; PS: tunable phase shifter; DC: directional coupler; and EDFA: erbium-doped fiber amplifier. (a) Tunable coupler (TC). (b) g[n], as defined in Eqs. (18), (32) and (33). The gates (or samplers), as shown, are for illustration only and should be removed when fabricating the device. These gates are moved to Fig. 2(d) for structural simplicity, without affecting the device performance. (c) y[n], as defined in Eqs. (15), (19), (34) and (35). (d) X[n] , as defined in Eqs. (26), (36) and (37), and X u [n]=X[n+N1] (n=0,1,,L1) as defined in Eq. (20d).
Fig. 3
Fig. 3 Magnitude response of the new ODFT design as a special case of the synthesized OCZT with r 0 = R 0 =1 , N=8 , L=7 , θ 0 = 50 , and ϕ 0 = 45 .

Tables (1)

Tables Icon

Table 1 The Tunable OCZT Architecture using the Simplified CZT Algorithm in this paper is Much Simpler than that using the Non-simplified CZT Algorithm Reported in [1]

Equations (61)

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

X(z)= n=0 N1 x[n] z n ,
X[k]= X(z) | z= z k = n=0 N1 x[n] z k n ; k=0,1,,L1,
z k =[ r 0 exp(j θ 0 ) ] [ R 0 exp(j ϕ 0 ) ] k ,
X[k]= n=0 N1 x[n] ( r 0 exp(j θ 0 ) ) n V nk ; k=0,1,,L1,
V= R 0 exp(j ϕ 0 ).
nk= 1 2 [ n 2 + k 2 (kn) 2 ]
X[k]= V k 2 /2 n=0 N1 g[n] V (kn) 2 /2 ; k=0,1,,L1,
g[n]=x[n] ( r 0 exp(j θ 0 ) ) n V n 2 /2 ; n=0,1,,N1.
X[n]= V n 2 /2 k=0 N1 g[k] V (nk) 2 /2 ; n=0,1,,L1.
h[n]= V n 2 /2 ,
h[nk]= V (nk) 2 /2 .
X[n]= V n 2 /2 y[n]; n=0,1,,L1,
y[n]= k=0 N1 g[k] h[nk]; n=0,1,,L1,
y[n]=g[n]h[n]; n=0,1,,L1,
h[n]= V n 2 /2 ; (N1)nL1.
h 1 [n]=h[n(N1)]= V (nN+1) 2 /2 ; 0nL+N2.
y[n]= k=0 N1 g[k] h 1 [nk]; n=0,1,,L+N2,
y[n]=g[n] h 1 [n]; n=0,1,,L+N2.
X[n]= V (nN+1) 2 /2 y[n]; n=0,1,,L+N2.
X u [n]=X[n+N1]; n=0,1,,L1.
g[n]=x[n]×[ a[n]exp(jα[n]) ]; n=0,1,,N1,
a[n]=( r 0 n )( R 0 n 2 /2 ),
α[n]=( n θ 0 + n 2 2 ϕ 0 ).
h 1 [n]=b[n]exp(jβ[n]); n=0,1,,L+N2,
b[n]= R 0 (nN+1) 2 /2 ,
β[n]=+ (nN+1) 2 2 ϕ 0 .
X[n]=y[n]×[ c[n]exp(jγ[n]) ]; n=0,1,,L+N2,
c[n]= R 0 (nN+1) 2 /2 ,
γ[n]= (nN+1) 2 2 ϕ 0 ,
X u [n]=X[n+N1]; n=0,1,,L1.
r 0 1 R 0 n/2 ; n=0,1,,N1,
R 0 1 r 0 2/n ; n=0,1,,N1.
b[n]= 1 c[n] ; n=0,1,,L+N2,
Design 1: if b[n]1 then c[n]1 and
Design 2: if b[n]1 then c[n]1.
0< R 0 1.
r 0 1.
X[n]=c [n] max [ y[n]× c [n]×exp(jγ[n]) ],
( G )( 1 N )( 1 L+N1 )( 1 L )( 1 c [n] max )( G )=1,
G= N L+N1 L c [n] max ,
C(k)=| C(k) |exp( jC(k) )=0.5[ exp( jφ(k) )1 ]
| C(k) |= 0.50.5cos( φ(k) )
φ n = cos 1 [ 12 | C n | 2 ].
C(k)= tan 1 [ sin(φ(k)) / ( cos(φ(k))1 ) ]
a[n]=| C a[n] |,
α [n]=α[n] C a[n] ,
b[n]=| C b[n] |,
β [n]=β[n] C b[n] ,
c [n]=| C c [n] |,
γ [n]=γ[n] C c [n] ,
R 0 1.
0< r 0 1.
h 1 [n]=b [n] max [ b [n]exp(jβ[n]) ],
b [n]=| C b [n] |,
β [n]=β[n] C b [n] ,
c[n]=| C c[n] |,
γ [n]=γ[n] C c[n] ,
G= N L+N1 L b [n] max .
X k (ω)= n=0 N1 exp( j θ k,n ) x(nT); k=0,1,,L1
X k (t)= n=0 N1 exp( j θ k,n ) [ δ(tnT)x(t) ]
H k (ω)= X k (ω) X(ω) = 1 N n=0 N1 exp( j θ k,n ) exp[ jnωT ]

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