Abstract

To the best of our knowledge, for the first time a programmable broadband rf transversal filter is proposed that operates on the principle of broadband optical spectral control implemented with a spatial light modulator input rf signal time delay and weight selection over a near-continuous signal space. Specifically, the filter uses a chirped fiber Bragg grating in combination with a two-dimensional digital micromirror device to enable a programmable rf filter. As a first step, a two-tap rf notch filter is demonstrated with a tuning range of 0.563–6.032 GHz with a 25-dB notch depth at test notch frequencies of 845 and 905 MHz. The proposed filter can find applications in diverse fields such as radar, communications, medicine, and test and measurement.

© 2004 Optical Society of America

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References

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  1. K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
    [CrossRef]
  2. S. Gweon, C. E. Lee, H. F. Taylor, “Wide-band fiber optic signal processor,” IEEE Photon. Technol. Lett. 1, 467–468 (1989).
    [CrossRef]
  3. D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
    [CrossRef]
  4. M. E. Frankel, R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7, 191–193 (1995).
    [CrossRef]
  5. D. B. Hunter, R. A. Minasian, “Reflectivity tapped fiber optic transversal filter using in-fiber Bragg gratings,” Electron. Lett. 31, 1010–1012 (1995).
    [CrossRef]
  6. D. B. Hunter, R. A. Minasian, P. A. Krug, “Tunable optical transversal filter based on chirped gratings,” Electron. Lett. 31, 2205–2207 (1995).
    [CrossRef]
  7. R. A. Soref, “Fiber grating prism for true time delay beam steering,” Fiber Integr. Opt. 15, 325–333 (1996).
    [CrossRef]
  8. J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
    [CrossRef]
  9. D. Pastor, J. Capmany, B. Ortega, “Broad-band tunable microwave transversal notch filter based on tunable uniform fiber Bragg gratings as slicing filters,” IEEE Photon. Technol. Lett. 13, 726–728 (2001).
    [CrossRef]
  10. W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photon. Technol. Lett. 13, 523–525 (2001).
    [CrossRef]
  11. F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
    [CrossRef]
  12. J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
    [CrossRef]
  13. N. A. Riza, “An optical transversal filter,” U.S. patent5,329,118 (12July1994).
  14. B. Moslehi, K. K. Chau, J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processor,” Opt. Eng. 32, 574–581 (1993).
    [CrossRef]
  15. D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
    [CrossRef]
  16. A. Ambardar, Analog and Digital Signal Processing, 2nd ed. (Brooks-Cole, Pacific Grove, Calif., 1999).
  17. N. A. Riza, M. J. Mughal, “Broadband optical equalizer using fault tolerant digital micromirrors,” Opt. Exp. 11, 1559–1565 (2003), http://www.opticsexpress.org .
    [CrossRef]

2003

J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
[CrossRef]

N. A. Riza, M. J. Mughal, “Broadband optical equalizer using fault tolerant digital micromirrors,” Opt. Exp. 11, 1559–1565 (2003), http://www.opticsexpress.org .
[CrossRef]

2001

D. Pastor, J. Capmany, B. Ortega, “Broad-band tunable microwave transversal notch filter based on tunable uniform fiber Bragg gratings as slicing filters,” IEEE Photon. Technol. Lett. 13, 726–728 (2001).
[CrossRef]

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photon. Technol. Lett. 13, 523–525 (2001).
[CrossRef]

1999

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[CrossRef]

1997

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
[CrossRef]

1996

R. A. Soref, “Fiber grating prism for true time delay beam steering,” Fiber Integr. Opt. 15, 325–333 (1996).
[CrossRef]

1995

M. E. Frankel, R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7, 191–193 (1995).
[CrossRef]

D. B. Hunter, R. A. Minasian, “Reflectivity tapped fiber optic transversal filter using in-fiber Bragg gratings,” Electron. Lett. 31, 1010–1012 (1995).
[CrossRef]

D. B. Hunter, R. A. Minasian, P. A. Krug, “Tunable optical transversal filter based on chirped gratings,” Electron. Lett. 31, 2205–2207 (1995).
[CrossRef]

1994

D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
[CrossRef]

1993

B. Moslehi, K. K. Chau, J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processor,” Opt. Eng. 32, 574–581 (1993).
[CrossRef]

1989

S. Gweon, C. E. Lee, H. F. Taylor, “Wide-band fiber optic signal processor,” IEEE Photon. Technol. Lett. 1, 467–468 (1989).
[CrossRef]

1985

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Ambardar, A.

A. Ambardar, Analog and Digital Signal Processing, 2nd ed. (Brooks-Cole, Pacific Grove, Calif., 1999).

Bennion, I.

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photon. Technol. Lett. 13, 523–525 (2001).
[CrossRef]

Capmany, J.

D. Pastor, J. Capmany, B. Ortega, “Broad-band tunable microwave transversal notch filter based on tunable uniform fiber Bragg gratings as slicing filters,” IEEE Photon. Technol. Lett. 13, 726–728 (2001).
[CrossRef]

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[CrossRef]

Chau, K. K.

B. Moslehi, K. K. Chau, J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processor,” Opt. Eng. 32, 574–581 (1993).
[CrossRef]

Chen, J. X.

J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
[CrossRef]

Coppinger, F.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
[CrossRef]

Cutler, C. C.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Dolfi, D.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

Durand, O.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

Esman, R. D.

M. E. Frankel, R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7, 191–193 (1995).
[CrossRef]

Frankel, M. E.

M. E. Frankel, R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7, 191–193 (1995).
[CrossRef]

Goodman, J. W.

B. Moslehi, K. K. Chau, J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processor,” Opt. Eng. 32, 574–581 (1993).
[CrossRef]

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Gweon, S.

S. Gweon, C. E. Lee, H. F. Taylor, “Wide-band fiber optic signal processor,” IEEE Photon. Technol. Lett. 1, 467–468 (1989).
[CrossRef]

Hodiak, J.

J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
[CrossRef]

Huignard, J.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

Hunter, D. B.

D. B. Hunter, R. A. Minasian, “Reflectivity tapped fiber optic transversal filter using in-fiber Bragg gratings,” Electron. Lett. 31, 1010–1012 (1995).
[CrossRef]

D. B. Hunter, R. A. Minasian, P. A. Krug, “Tunable optical transversal filter based on chirped gratings,” Electron. Lett. 31, 2205–2207 (1995).
[CrossRef]

Jackson, K. P.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Jalali, B.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
[CrossRef]

Johns, S.

D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
[CrossRef]

Keefer, C.

D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
[CrossRef]

Krug, P. A.

D. B. Hunter, R. A. Minasian, P. A. Krug, “Tunable optical transversal filter based on chirped gratings,” Electron. Lett. 31, 2205–2207 (1995).
[CrossRef]

Laude, V.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

Lee, C. E.

S. Gweon, C. E. Lee, H. F. Taylor, “Wide-band fiber optic signal processor,” IEEE Photon. Technol. Lett. 1, 467–468 (1989).
[CrossRef]

Minasian, R. A.

D. B. Hunter, R. A. Minasian, P. A. Krug, “Tunable optical transversal filter based on chirped gratings,” Electron. Lett. 31, 2205–2207 (1995).
[CrossRef]

D. B. Hunter, R. A. Minasian, “Reflectivity tapped fiber optic transversal filter using in-fiber Bragg gratings,” Electron. Lett. 31, 1010–1012 (1995).
[CrossRef]

Moslehi, B.

B. Moslehi, K. K. Chau, J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processor,” Opt. Eng. 32, 574–581 (1993).
[CrossRef]

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Mughal, M. J.

N. A. Riza, M. J. Mughal, “Broadband optical equalizer using fault tolerant digital micromirrors,” Opt. Exp. 11, 1559–1565 (2003), http://www.opticsexpress.org .
[CrossRef]

Newton, S. A.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Norton, D.

D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
[CrossRef]

Ortega, B.

D. Pastor, J. Capmany, B. Ortega, “Broad-band tunable microwave transversal notch filter based on tunable uniform fiber Bragg gratings as slicing filters,” IEEE Photon. Technol. Lett. 13, 726–728 (2001).
[CrossRef]

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[CrossRef]

Pastor, D.

D. Pastor, J. Capmany, B. Ortega, “Broad-band tunable microwave transversal notch filter based on tunable uniform fiber Bragg gratings as slicing filters,” IEEE Photon. Technol. Lett. 13, 726–728 (2001).
[CrossRef]

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[CrossRef]

Riza, N. A.

N. A. Riza, M. J. Mughal, “Broadband optical equalizer using fault tolerant digital micromirrors,” Opt. Exp. 11, 1559–1565 (2003), http://www.opticsexpress.org .
[CrossRef]

N. A. Riza, “An optical transversal filter,” U.S. patent5,329,118 (12July1994).

Shaw, H. J.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Soref, R.

D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
[CrossRef]

Soref, R. A.

R. A. Soref, “Fiber grating prism for true time delay beam steering,” Fiber Integr. Opt. 15, 325–333 (1996).
[CrossRef]

Tabourel, J.

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

Taylor, H. F.

S. Gweon, C. E. Lee, H. F. Taylor, “Wide-band fiber optic signal processor,” IEEE Photon. Technol. Lett. 1, 467–468 (1989).
[CrossRef]

Trinh, P. D.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
[CrossRef]

Tur, M.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

Williams, J. A. R.

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photon. Technol. Lett. 13, 523–525 (2001).
[CrossRef]

Wu, Y.

J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
[CrossRef]

Yegnanarayanan, S.

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
[CrossRef]

Yu, P. K. L.

J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
[CrossRef]

Zhang, W.

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photon. Technol. Lett. 13, 523–525 (2001).
[CrossRef]

Electron. Lett.

D. B. Hunter, R. A. Minasian, “Reflectivity tapped fiber optic transversal filter using in-fiber Bragg gratings,” Electron. Lett. 31, 1010–1012 (1995).
[CrossRef]

D. B. Hunter, R. A. Minasian, P. A. Krug, “Tunable optical transversal filter based on chirped gratings,” Electron. Lett. 31, 2205–2207 (1995).
[CrossRef]

Fiber Integr. Opt.

R. A. Soref, “Fiber grating prism for true time delay beam steering,” Fiber Integr. Opt. 15, 325–333 (1996).
[CrossRef]

IEEE Photon. Technol. Lett.

D. Pastor, J. Capmany, B. Ortega, “Broad-band tunable microwave transversal notch filter based on tunable uniform fiber Bragg gratings as slicing filters,” IEEE Photon. Technol. Lett. 13, 726–728 (2001).
[CrossRef]

W. Zhang, J. A. R. Williams, I. Bennion, “Polarization synthesized optical transversal filter employing high birefringence fiber gratings,” IEEE Photon. Technol. Lett. 13, 523–525 (2001).
[CrossRef]

F. Coppinger, S. Yegnanarayanan, P. D. Trinh, B. Jalali, “Continuously tunable photonic radio-frequency notch filter,” IEEE Photon. Technol. Lett. 9, 339–341 (1997).
[CrossRef]

J. X. Chen, Y. Wu, J. Hodiak, P. K. L. Yu, “A novel digitally tunable microwave-photonic notch filter using differential group-delay module,” IEEE Photon. Technol. Lett. 15, 284–286 (2003).
[CrossRef]

S. Gweon, C. E. Lee, H. F. Taylor, “Wide-band fiber optic signal processor,” IEEE Photon. Technol. Lett. 1, 467–468 (1989).
[CrossRef]

D. Norton, S. Johns, C. Keefer, R. Soref, “Tunable microwave filtering using high dispersion fiber time delays,” IEEE Photon. Technol. Lett. 6, 831–832 (1994).
[CrossRef]

M. E. Frankel, R. D. Esman, “Fiber-optic tunable microwave transversal filter,” IEEE Photon. Technol. Lett. 7, 191–193 (1995).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

K. P. Jackson, S. A. Newton, B. Moslehi, M. Tur, C. C. Cutler, J. W. Goodman, H. J. Shaw, “Optical fiber delay-line signal processing,” IEEE Trans. Microwave Theory Tech. 33, 193–210 (1985).
[CrossRef]

D. Dolfi, J. Tabourel, O. Durand, V. Laude, J. Huignard, “Optical architecture for programmable filtering and correlation of microwave signals,” IEEE Trans. Microwave Theory Tech. 45, 1467–1471 (1997).
[CrossRef]

J. Capmany, D. Pastor, B. Ortega, “New and flexible fiber-optic delay-line filters using chirped Bragg gratings and laser arrays,” IEEE Trans. Microwave Theory Tech. 47, 1321–1326 (1999).
[CrossRef]

Opt. Eng.

B. Moslehi, K. K. Chau, J. W. Goodman, “Optical amplifiers and liquid-crystal shutters applied to electrically reconfigurable fiber optic signal processor,” Opt. Eng. 32, 574–581 (1993).
[CrossRef]

Opt. Exp.

N. A. Riza, M. J. Mughal, “Broadband optical equalizer using fault tolerant digital micromirrors,” Opt. Exp. 11, 1559–1565 (2003), http://www.opticsexpress.org .
[CrossRef]

Other

A. Ambardar, Analog and Digital Signal Processing, 2nd ed. (Brooks-Cole, Pacific Grove, Calif., 1999).

N. A. Riza, “An optical transversal filter,” U.S. patent5,329,118 (12July1994).

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Figures (5)

Fig. 1
Fig. 1

Proposed programmable broadband rf transversal filter with compact fiber-optics and SLM. M, high-speed optical intensity modulator; BOS, broadband optical source; τ d , fixed-path optical delay between odd and even wavelengths of the interleaver; I, interleaver; DA, differential amplifier; E, equalizer optics; C 1 and C 2, optical circulators; G, grating; C, cylindrical lens; PD1 and PD2, photodetectors; θ c , grating Bragg angle; F, focal length of C; FL, fiber lens.

Fig. 2
Fig. 2

Calculated rf resolution over the entire band of operation of the demonstrated filter. The left y axis represents the absolute frequency resolution in megahertz (solid curve) and the right y axis shows the resolution in terms of percentage of the operating frequency (dashed curve).

Fig. 3
Fig. 3

Time-domain impulse response h(t) of the demonstrated rf notch filter generated by the OSA where the upper x axis is the λ ji wavelength axis and the lower x axis is the mapped time-delay axis t.

Fig. 4
Fig. 4

Frequency-domain impulse response H(f) of the demonstrated rf notch filter response with a null set at 845 MHz. The solid curve is the calculated response of the rf filter after we take the fast Fourier transform of the measured impulse response in the time domain (i.e., shown in Fig. 3), and the dotted curve is the measured frequency response taken by a rf spectrum analyzer with a rf sweep input to the filter.

Fig. 5
Fig. 5

Frequency-domain impulse response H(f) of the demonstrated rf notch filter response with a null set at 0.905 GHz showing the tunability feature of the demonstrated rf filter.

Equations (8)

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

rt=n=0N-1 Anst-nτ,
rt=n=01 Ast-nτ=Ast+st-τ.
ht=Aδt+τ/2+δt-τ/2,
Hf=2A cosπfτ.
Hf=2 sinNπfτN sinπfτ.
ht=j=1Ni=-M/2M/2 Ajiλjiδt+τji/2.
ht=i=-M/2M/2 A1iλ1iδt+τ1i/2+i=-M/2M/2 A2iλ2iδt-τ2i/2.
Hf=i=-M/2M/2 Aiλicosπfτi.

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