Methods for computation-free wideband spectral correlation and analysis
An apparatus for generating a set of spectral correlation coefficients of an input signal includes: a master laser configured to generate an optical frequency comb signal; a first optical modulator configured to modulate the optical frequency comb signal with an input signal to generate a plurality of spectral copies of the input signal; a dispersive element configured to delay the plurality of spectral copies of the input signal by a wavelength-dependent time delay; a second optical modulator configured to modulate the delayed plurality of spectral copies with a conjugate of the input signal; and an optical comb filter configured to integrate the conjugate modulated plurality of spectral copies of the input signal to generate a set of cyclic autocorrelation coefficients.
1. An apparatus comprising:
a master laser configured to generate an optical frequency comb signal;
a first optical modulator configured to modulate the optical frequency comb signal with an input signal to generate a plurality of spectral copies of the input signal;
a dispersive element configured to delay the plurality of spectral copies of the input signal by a wavelength-dependent time delay to generate a delayed plurality of spectral copies of the input signal;
a second optical modulator configured to modulate the delayed plurality of spectral copies of the input signal with a conjugate of the input signal to generate a conjugate modulated delayed plurality of spectral copies of the input signal; and
an optical comb filter configured to integrate the conjugate modulated delayed plurality of spectral copies of the input signal to generate a set of cross-ambiguity function (CAF) correlation coefficients.
2. The apparatus of claim 1 , wherein the first optical modulator and the second optical modulator comprise amplitude modulators.
3. The apparatus of claim 1 , further comprising:
a local oscillator configured to generate a swept frequency;
a third optical modulator configured to modulate an optical signal generated by the master laser with the swept frequency from the local oscillator to generate swept optical sampling signals;
a wavelength demultiplexer configured to combine the swept optical sampling signals and the integrated conjugate modulated delayed plurality of spectral copies of the input signal such that each of the swept optical sampling signals is associated with a corresponding one of the integrated conjugate modulated delayed plurality of spectral copies of the input signal; and
a plurality of detectors configured to detect the set of CAF correlation coefficients for all time delays of an associated tone from the integrated conjugate modulated delayed plurality of spectral copies of the input signal and to output the set of CAF correlation coefficients.
4. The apparatus of claim 3 , wherein the third optical modulator comprises a single side band modulator.
5. The apparatus of claim 3 , wherein the plurality of detectors comprises coherent receivers.
6. A method comprising:
generating an optical frequency comb signal from an optical signal generated by a master laser;
generating a plurality of spectral copies of a first signal by modulating the optical frequency comb signal with the first signal;
delaying the plurality of spectral copies of the first signal by a wavelength-dependent time delay to generate a delayed plurality of spectral copies of the first signal;
modulating the delayed plurality of spectral copies of the first signal with a conjugate of a second signal to generate a conjugate modulated delayed plurality of spectral copies of the first signal, the second signal being from a common transmission source as the first signal; and
generating a set of cross-ambiguity function (CAF) correlation coefficients by integrating the conjugate modulated delayed plurality of spectral copies of the first signal.
7. The method of claim 6 , wherein the optical frequency comb signal and the delayed plurality of spectral copies of the first signal are amplitude modulated.
8. The method of claim 6 , further comprising:
generating a swept frequency;
modulating the optical signal generated by the master laser with the swept frequency to generate swept optical sampling signals;
combining the swept optical sampling signals and the integrated conjugate modulated delayed plurality of spectral copies of the first signal such that each of the swept optical sampling signals is associated with a corresponding one of the integrated conjugate modulated delayed plurality of spectral copies of the first signal;
detecting the set of CAF correlation coefficients for all time delays of an associated tone from the integrated conjugate modulated delayed plurality of spectral copies of the first signal; and
outputting the set of CAF correlation coefficients.
9. The method of claim 8 , wherein the optical signal generated by the master laser is single side band modulated.
10. The method of claim 8 , wherein detecting the set of CAF correlation coefficients comprises performing coherent detection.
11. A method comprising:
generating an optical frequency comb signal from an optical signal generated by a master laser;
generating a plurality of spectral copies of a first signal by modulating the optical frequency comb signal with the first signal;
delaying the plurality of spectral copies of the first signal by a wavelength-dependent time delay to generate a delayed plurality of spectral copies of the first signal;
modulating the delayed plurality of spectral copies of the first signal with a conjugate of a second signal to generate a conjugate modulated delayed plurality of spectral copies of the first signal, the second signal being from a common transmission source as the first signal;
integrating the conjugate modulated delayed plurality of spectral copies of the first signal to generate an integrated conjugate modulated delayed plurality of spectral copies of the first signal;
generating a swept frequency;
modulating the optical signal generated by the master laser with the swept frequency to generate swept optical sampling signals;
combining the swept optical sampling signals and the integrated conjugate modulated delayed plurality of spectral copies of the first signal such that each of the swept optical sampling signals is associated with a corresponding one of the integrated conjugate modulated delayed plurality of spectral copies of the first signal;
detecting a set of Wigner coefficients for a Wigner function in an optical domain for all time delays of an associated tone from the integrated conjugate modulated delayed plurality of spectral copies of the first signal; and
outputting the set of Wigner coefficients.
12. The method of claim 11 , wherein:
the second signal is a conjugate of the first signal, and
the Wigner function is a cyclic autocorrelation function.
13. The method of claim 11 , wherein:
the second signal is a conjugate of a signal different from the first signal received from the common transmission source, and
the Wigner function is a cross-ambiguity function (CAF).
14. The method of claim 11 , wherein the optical frequency comb signal and the delayed plurality of spectral copies of the first signal are amplitude modulated.
15. The method of claim 11 , wherein the optical signal generated by the master laser is single side band modulated.
16. The method of claim 11 , wherein detecting the set of Wigner coefficients comprises performing coherent detection.
17. The apparatus of claim 3 , wherein the swept optical sampling signals sweep at a lower rate than a frequency of the optical signal generated by the master laser.
18. The apparatus of claim 3 , wherein the swept optical sampling signals and the optical frequency comb signal have a common frequency pitch.
19. The method of claim 8 , wherein the swept optical sampling signals sweep at a lower rate than a frequency of the optical signal generated by the master laser.
20. The method of claim 8 , wherein the swept optical sampling signals and the optical frequency comb signal have a common frequency pitch.