Abstract

Traditional photonics-assisted real-time Fourier transform (RTFT) usually suffers from limited chromatic dispersion, huge volume, or large time delay and attendant loss. In this paper we propose frequency-to-time mapping (FTM) by spectrally-discrete dispersion to increase frequency sensitivity greatly. The novel media has periodic ON/OFF intensity frequency response while quadratic phase distribution along disconnected channels, which de-chirps matched optical input to repeated Fourier-transform-limited output. Real-time FTM is then obtained within each period. Since only discrete phase retardation rather than continuously-changed true time delay is required, huge equivalent dispersion is then available by compact device. Such FTM is theoretically analyzed, and implementation by cascaded optical ring resonators is proposed. After a numerical example, our theory is demonstrated by a proof-of-concept experiment, where a single loop containing 0.5-meters-long fiber is used. FTM under 400-MHz unambiguous bandwidth and 25-MHz resolution is reported. Highly-sensitive and linear mapping is achieved with 6.25 ps/MHz, equivalent to ~4.6 × 104-km standard single mode fiber. Extended instantaneous bandwidth is expected by ring cascading. Our proposal may provide a promising method for real-time, low-latency Fourier transform.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (1)

2014 (1)

C. Zhang, X. Wei, M. E. Marhic, and K. K. Y. Wong, “Ultrafast and versatile spectroscopy by temporal Fourier transform,” Sci. Rep. 4(1), 5351 (2014).
[Crossref] [PubMed]

2013 (2)

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

C. Wang and J. P. Yao, “Ultrahigh-resolution photonic-assisted microwave frequency identification based on temporal channelization,” IEEE Trans. Microw. Theory Tech. 61(12), 4275–4282 (2013).
[Crossref]

2012 (1)

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

2011 (1)

H. Nan, Y. Gu, and H. Zhang, “Optical Analog-to-Digital Conversion System Based on Compressive Sampling,” IEEE Photonics Technol. Lett. 23(2), 67–69 (2011).
[Crossref]

2010 (1)

2009 (2)

2008 (2)

H. Chi, X. Zou, and J. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photonics Technol. Lett. 20(14), 1249–1251 (2008).
[Crossref]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

2007 (3)

2006 (2)

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

J. Howe and C. Xu, “Ultrafast optical signal processing based upon space–time dualities,” J. Lightwave Technol. 24(7), 2649–2662 (2006).
[Crossref]

2004 (1)

2003 (1)

2001 (1)

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

2000 (1)

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000).
[Crossref]

1983 (1)

Aditya, S.

Ahn, T. J.

Austin, M. W.

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

Azaña, J.

Brook, J.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Bui, L. A.

Canning, J.

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

Capmany, J.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Chatellus, H.

Chen, L.

Chi, H.

H. Chi, X. Zou, and J. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photonics Technol. Lett. 20(14), 1249–1251 (2008).
[Crossref]

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Clark, T. R.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

Cortés, L.

Dai, Y.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

Davis, R.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Dennis, M. L.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

Duan, Y.

Eggleton, B. J.

Emami, H.

Fainman, Y.

Fu, S.

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

Gu, Y.

H. Nan, Y. Gu, and H. Zhang, “Optical Analog-to-Digital Conversion System Based on Compressive Sampling,” IEEE Photonics Technol. Lett. 23(2), 67–69 (2011).
[Crossref]

Han, Y.

Howe, J.

Jalali, B.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Y. Han and B. Jalali, “Photonic Time-Stretched Analog-to-Digital Converter: Fundamental Concepts and Practical Considerations,” J. Lightwave Technol. 21(12), 3085–3103 (2003).
[Crossref]

Jannson, T.

Jung, T.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Kieffer, J. C.

Lembo, L.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Li, J.

Lin, J.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

Lindsay, A. C.

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

Lodenkamper, R.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Lucarelli, D. G.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

Marhic, M. E.

C. Zhang, X. Wei, M. E. Marhic, and K. K. Y. Wong, “Ultrafast and versatile spectroscopy by temporal Fourier transform,” Sci. Rep. 4(1), 5351 (2014).
[Crossref] [PubMed]

McKenna, T. P.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

Mitchell, A.

L. A. Bui, M. D. Pelusi, T. D. Vo, N. Sarkhosh, H. Emami, B. J. Eggleton, and A. Mitchell, “Instantaneous frequency measurement system using optical mixing in highly nonlinear fiber,” Opt. Express 17(25), 22983–22991 (2009).
[Crossref] [PubMed]

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

Muriel, M. A.

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000).
[Crossref]

Nan, H.

H. Nan, Y. Gu, and H. Zhang, “Optical Analog-to-Digital Conversion System Based on Compressive Sampling,” IEEE Photonics Technol. Lett. 23(2), 67–69 (2011).
[Crossref]

Nanzer, J. A.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

Niu, J.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

Novak, D.

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

Panasenko, D.

Park, Y.

Pelusi, M. D.

Saperstein, R. E.

Sarkhosh, N.

Sharp, M. D.

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

Shum, P. P.

Solli, D. R.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Sun, X.

Valley, G. C.

Vo, T. D.

Wang, C.

C. Wang and J. P. Yao, “Ultrahigh-resolution photonic-assisted microwave frequency identification based on temporal channelization,” IEEE Trans. Microw. Theory Tech. 61(12), 4275–4282 (2013).
[Crossref]

Wang, R.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

Wang, W.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Wei, X.

C. Zhang, X. Wei, M. E. Marhic, and K. K. Y. Wong, “Ultrafast and versatile spectroscopy by temporal Fourier transform,” Sci. Rep. 4(1), 5351 (2014).
[Crossref] [PubMed]

Winnall, S. T.

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

Wong, K. K. Y.

C. Zhang, X. Wei, M. E. Marhic, and K. K. Y. Wong, “Ultrafast and versatile spectroscopy by temporal Fourier transform,” Sci. Rep. 4(1), 5351 (2014).
[Crossref] [PubMed]

Wu, M.

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

Xia, L.

Xie, X.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

Xu, C.

Xu, K.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

J. Zhou, S. Fu, P. P. Shum, S. Aditya, L. Xia, J. Li, X. Sun, and K. Xu, “Photonic measurement of microwave frequency based on phase modulation,” Opt. Express 17(9), 7217–7221 (2009).
[Crossref] [PubMed]

Yan, L.

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

Yao, J.

H. Chi, X. Zou, and J. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photonics Technol. Lett. 20(14), 1249–1251 (2008).
[Crossref]

Yao, J. P.

C. Wang and J. P. Yao, “Ultrahigh-resolution photonic-assisted microwave frequency identification based on temporal channelization,” IEEE Trans. Microw. Theory Tech. 61(12), 4275–4282 (2013).
[Crossref]

Zhang, C.

Zhang, H.

H. Nan, Y. Gu, and H. Zhang, “Optical Analog-to-Digital Conversion System Based on Compressive Sampling,” IEEE Photonics Technol. Lett. 23(2), 67–69 (2011).
[Crossref]

Zhang, X.

Zhou, H.

Zhou, J.

Zhou, X.

Zou, X.

H. Chi, X. Zou, and J. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photonics Technol. Lett. 20(14), 1249–1251 (2008).
[Crossref]

IEEE J. Quantum Electron. (1)

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000).
[Crossref]

IEEE Photonics J. (1)

X. Xie, Y. Dai, K. Xu, J. Niu, R. Wang, L. Yan, and J. Lin, “Broadband photonic RF channelization based on coherent optical frequency combs and I/Q demodulators,” IEEE Photonics J. 4(4), 1196–1202 (2012).
[Crossref]

IEEE Photonics Technol. Lett. (2)

H. Nan, Y. Gu, and H. Zhang, “Optical Analog-to-Digital Conversion System Based on Compressive Sampling,” IEEE Photonics Technol. Lett. 23(2), 67–69 (2011).
[Crossref]

H. Chi, X. Zou, and J. Yao, “An approach to the measurement of microwave frequency based on optical power monitoring,” IEEE Photonics Technol. Lett. 20(14), 1249–1251 (2008).
[Crossref]

IEEE Trans. Microw. Theory Tech. (3)

S. T. Winnall, A. C. Lindsay, M. W. Austin, J. Canning, and A. Mitchell, “A microwave channelizer and spectroscope based on an integrated optical Bragg-grating Fabry-Perot and integrated hybrid Fresnel lens system,” IEEE Trans. Microw. Theory Tech. 54(2), 868–872 (2006).
[Crossref]

W. Wang, R. Davis, T. Jung, R. Lodenkamper, L. Lembo, J. Brook, and M. Wu, “Characterization of a coherent optical RF channelizer based on a diffraction grating,” IEEE Trans. Microw. Theory Tech. 49(10), 1996–2001 (2001).
[Crossref]

C. Wang and J. P. Yao, “Ultrahigh-resolution photonic-assisted microwave frequency identification based on temporal channelization,” IEEE Trans. Microw. Theory Tech. 61(12), 4275–4282 (2013).
[Crossref]

J. Lightwave Technol. (2)

Nat. Photonics (3)

J. Capmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007).
[Crossref]

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nat. Photonics 7(2), 102–112 (2013).
[Crossref]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength-time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[Crossref]

Opt. Express (6)

Opt. Lett. (2)

Optica (1)

Sci. Rep. (1)

C. Zhang, X. Wei, M. E. Marhic, and K. K. Y. Wong, “Ultrafast and versatile spectroscopy by temporal Fourier transform,” Sci. Rep. 4(1), 5351 (2014).
[Crossref] [PubMed]

Other (1)

T. P. McKenna, M. D. Sharp, D. G. Lucarelli, J. A. Nanzer, M. L. Dennis, and T. R. Clark, “Wideband photonic compressive sampling analog-to-digital converter for RF spectrum estimation,” 2013 Optical Fiber Communication Conference and Exposition and the National Fiber Optic Engineers Conference (OFC/NFOEC), Anaheim, CA, 2013, pp. 1–3.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Comparison between pulse de-chirping by continuous dispersion and by discrete dispersion. In discrete one, quadratic-phase-distributed but intensity-sliced frequency response results in periodic output of de-chirped pulse.
Fig. 2
Fig. 2 A comb filter example based on optical ring resonators which could approximate the desired discrete dispersion by individual phase control instead of huge-volume real dispersion. fm is the resonant frequency of the corresponding ring.
Fig. 3
Fig. 3 (a) Simulated power transmission spectrum of the proposed ring-based discrete dispersion shown in Fig. 2. (b) Blue line: the corresponding phase response; red dot: wrapped phase retardation at each transmission peak; red dotted line: wrapped quadratic fit.
Fig. 4
Fig. 4 Simulated FTM through the proposed ring-based FTM. (a) Output waveform under zero (black line) and 50-MHz frequency shift (dark blue line). (b) Periodic FTM output. (c) Zoom in of one period; waveform with different color corresponds to specific frequency shift. (d) The calculated frequency to delay mapping (colorful dots) and theory prediction (red line).
Fig. 5
Fig. 5 Experiment setup. e-AWG: electronic AWG; e-LO: electronic local oscillation; RF amp: RF amplifier; PM: phase modulator; OC: optical coupler; OSC: real-time oscilloscope; red line: optical fiber; blue line: electronic cable. Inset shows the measured power transmission of the passive fiber loop.
Fig. 6
Fig. 6 (a) Output waveforms when single RF tone with four different frequencies around 20 GHz is input. “Reference” pulses are aligned in time. No averaging is performed. (b) Measured driving-frequency-dependent time delay (dots) of the “FTM” pulse offset from “reference” pulse. Line: theoretical prediction. Four sub-plots show FTM at different unambiguous 400-MHz bandwidth.
Fig. 7
Fig. 7 Output waveforms when three driving frequencies, separated by 25 MHz, are input individually. “Reference” pulses are aligned in time. No averaging is performed.

Equations (6)

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[ x( t )exp( i t 2 / 2 β 2 ) ] F 1 exp( i β 2 Ω 2 /2 ) X( t/ β 2 )exp( i t 2 / 2 β 2 )
RBW=1/ ( 2π β 2 B O )
[ x( t )exp( i t 2 / 2 β 2 ) ] F 1 exp( i β 2 Ω 2 /2 ) k P( Ωk2 πFSR DD ) [ X( t/ β 2 )exp( i t 2 / 2 β 2 ) ] F 1 k P( Ωk2 πFSR DD ) k p( k/ FSR DD )X[ ( tk/ FSR DD )/ β 2 ]exp[ i ( tk/ FSR DD ) 2 / 2 β 2 ]
M= B FTM / FSR DD
β 2 =M/ ( 2π B FTM 2 ) , and ϕ k =kMπ+ π k 2 /M
B O = B FTM 2 / ( MRBW ) , and T O =1/ RBW

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