Abstract

Time-frequency decomposition techniques, borrowed from the signal-processing field, have been adapted and applied to the analysis of 2D oscillating signals. While the Fourier-analysis techniques available so far are able to interpret the information content of the oscillating signal only in terms of its frequency components, the time-frequency transforms (TFT) proposed in this work can instead provide simultaneously frequency and time resolution, unveiling the dynamics of the relevant beating components, and supplying a valuable help in their interpretation. In order to fully exploit the potentiality of this method, several TFTs have been tested in the analysis of sample 2D data. Possible artifacts and sources of misinterpretation have been identified and discussed.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Optimization and selection of time-frequency transforms for wave-packet analysis in ultrafast spectroscopy

Andrea Volpato and Elisabetta Collini
Opt. Express 27(3) 2975-2987 (2019)

Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study

Yae-lin Sheu, Hau-tieng Wu, and Liang-Yan Hsu
Opt. Express 23(23) 30459-30482 (2015)

Short-time Fourier transform and wavelet transform with Fourier-domain processing

F. T. S. Yu and Guowen Lu
Appl. Opt. 33(23) 5262-5270 (1994)

References

  • View by:
  • |
  • |
  • |

  1. S. Mukamel, Principles of Nonlinear Optics and Spectroscopy (Oxford University, 1995).
  2. E. Collini, “Spectroscopic signatures of quantum-coherent energy transfer,” Chem. Soc. Rev. 42(12), 4932–4947 (2013).
    [Crossref] [PubMed]
  3. Y.-C. Cheng and G. R. Fleming, “Coherence quantum beats in two-dimensional electronic spectroscopy,” J. Phys. Chem. A 112(18), 4254–4260 (2008).
    [Crossref] [PubMed]
  4. A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
    [Crossref] [PubMed]
  5. E. Collini and G. D. Scholes, “Coherent intrachain energy migration in a conjugated polymer at room temperature,” Science 323(5912), 369–373 (2009).
    [Crossref] [PubMed]
  6. E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
    [Crossref] [PubMed]
  7. E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
    [Crossref]
  8. Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
    [Crossref] [PubMed]
  9. V. Tiwari, W. K. Peters, and D. M. Jonas, “Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework,” Proc. Natl. Acad. Sci. USA 110(4), 1203–1208 (2013).
    [Crossref] [PubMed]
  10. S. F. Huelga and M. B. Plenio, “Vibrations, quanta and biology,” Contemp. Phys. 54(4), 181–207 (2013).
    [Crossref]
  11. A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
    [Crossref] [PubMed]
  12. G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
    [Crossref] [PubMed]
  13. N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
    [Crossref] [PubMed]
  14. A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
    [Crossref]
  15. X. Wu and T. Liu, “Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution,” J. Appl. Geophys. 68(3), 386–393 (2009).
    [Crossref]
  16. E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
    [Crossref] [PubMed]
  17. K. Gröchenig, Foundations of Time-Frequency Analysis (Springer Science, 2001).
  18. T. Jo Lynn and A. Z. Bin Sha’ameri, “Signal analysis and classification of digital communication signals using adaptive smooth-windowed Wigner-Ville distribution,” in Proceedings of IEEE Conference on Telecommunication Technologies (IEEE, 2008), pp. 260–266.
  19. M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37–R40 (1996).
    [Crossref] [PubMed]
  20. T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 332(3-4), 324–330 (2000).
    [Crossref]
  21. D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
    [Crossref] [PubMed]
  22. T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem. Rec. 11(2), 99–116 (2011).
    [Crossref] [PubMed]
  23. A. Yabushita and T. Kobayashi, “Primary conformation change in bacteriorhodopsin on photoexcitation,” Biophys. J. 96(4), 1447–1461 (2009).
    [Crossref] [PubMed]
  24. S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice Hall, 1988).
  25. S. L. Marple, Digital Spectral Analysis: With Applications (Prentice Hall, 1987).
  26. L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7(5), 781–786 (1966).
    [Crossref]
  27. C. H. Page, “Instantaneous power spectra,” J. Appl. Phys. 23(1), 103–106 (1952).
    [Crossref]
  28. A. W. Rihaczek, “Signal energy distribution in time and frequency,” IEEE Trans. Inf. Theory 14(3), 369–374 (1968).
    [Crossref]
  29. Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoust. Speech 38(7), 1084–1091 (1990).
    [Crossref]
  30. D. Gabor, “Theory of communication,” J. of IEEE 93, 429–457 (1943).
  31. J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
    [Crossref] [PubMed]
  32. R. D. Hippenstiel and P. M. de Oliveira, “Time-varying spectral estimation using the instantaneous power spectrum (IPS),” IEEE Trans. Acoust. Speech 38(10), 1752–1759 (1990).
    [Crossref]
  33. H. Margenau and R. N. Hill, “Correlation between measurements in quantum theory,” Prog. Theor. Phys. 26(5), 722–738 (1961).
    [Crossref]
  34. E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40(5), 749–759 (1932).
    [Crossref]
  35. J. Ville, “Théorie et application de la notion de signal analytique,” Câbles et Transmissions 2eA, 61–74 (1948).
  36. L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77(7), 941–981 (1989).
    [Crossref]
  37. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “Wigner distribution - A tool for time-frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).
  38. H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech 37(6), 862–871 (1989).
    [Crossref]
  39. S. Qian and C. Dapang, “Joint time-frequency analysis,” IEEE Signal Process. Mag. 16(2), 52–67 (1999).
    [Crossref]

2014 (3)

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

2013 (6)

V. Tiwari, W. K. Peters, and D. M. Jonas, “Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework,” Proc. Natl. Acad. Sci. USA 110(4), 1203–1208 (2013).
[Crossref] [PubMed]

S. F. Huelga and M. B. Plenio, “Vibrations, quanta and biology,” Contemp. Phys. 54(4), 181–207 (2013).
[Crossref]

E. Collini, “Spectroscopic signatures of quantum-coherent energy transfer,” Chem. Soc. Rev. 42(12), 4932–4947 (2013).
[Crossref] [PubMed]

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

2012 (2)

N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
[Crossref] [PubMed]

A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
[Crossref] [PubMed]

2011 (1)

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem. Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

2010 (1)

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

2009 (3)

A. Yabushita and T. Kobayashi, “Primary conformation change in bacteriorhodopsin on photoexcitation,” Biophys. J. 96(4), 1447–1461 (2009).
[Crossref] [PubMed]

X. Wu and T. Liu, “Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution,” J. Appl. Geophys. 68(3), 386–393 (2009).
[Crossref]

E. Collini and G. D. Scholes, “Coherent intrachain energy migration in a conjugated polymer at room temperature,” Science 323(5912), 369–373 (2009).
[Crossref] [PubMed]

2008 (1)

Y.-C. Cheng and G. R. Fleming, “Coherence quantum beats in two-dimensional electronic spectroscopy,” J. Phys. Chem. A 112(18), 4254–4260 (2008).
[Crossref] [PubMed]

2007 (1)

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

2001 (1)

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

2000 (1)

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 332(3-4), 324–330 (2000).
[Crossref]

1999 (1)

S. Qian and C. Dapang, “Joint time-frequency analysis,” IEEE Signal Process. Mag. 16(2), 52–67 (1999).
[Crossref]

1996 (1)

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37–R40 (1996).
[Crossref] [PubMed]

1990 (2)

Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoust. Speech 38(7), 1084–1091 (1990).
[Crossref]

R. D. Hippenstiel and P. M. de Oliveira, “Time-varying spectral estimation using the instantaneous power spectrum (IPS),” IEEE Trans. Acoust. Speech 38(10), 1752–1759 (1990).
[Crossref]

1989 (2)

L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech 37(6), 862–871 (1989).
[Crossref]

1980 (1)

T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “Wigner distribution - A tool for time-frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

1968 (1)

A. W. Rihaczek, “Signal energy distribution in time and frequency,” IEEE Trans. Inf. Theory 14(3), 369–374 (1968).
[Crossref]

1966 (1)

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7(5), 781–786 (1966).
[Crossref]

1961 (1)

H. Margenau and R. N. Hill, “Correlation between measurements in quantum theory,” Prog. Theor. Phys. 26(5), 722–738 (1961).
[Crossref]

1952 (1)

C. H. Page, “Instantaneous power spectra,” J. Appl. Phys. 23(1), 103–106 (1952).
[Crossref]

1948 (1)

J. Ville, “Théorie et application de la notion de signal analytique,” Câbles et Transmissions 2eA, 61–74 (1948).

1943 (1)

D. Gabor, “Theory of communication,” J. of IEEE 93, 429–457 (1943).

1932 (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40(5), 749–759 (1932).
[Crossref]

Ahn, T.-K.

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Almeida, J.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

Atlas, L. E.

Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoust. Speech 38(7), 1084–1091 (1990).
[Crossref]

Augulis, R.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Bin Sha’ameri, A. Z.

T. Jo Lynn and A. Z. Bin Sha’ameri, “Signal analysis and classification of digital communication signals using adaptive smooth-windowed Wigner-Ville distribution,” in Proceedings of IEEE Conference on Telecommunication Technologies (IEEE, 2008), pp. 260–266.

Blankenship, R. E.

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Brumer, P.

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

Calhoun, T. R.

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Castro, E.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

Caycedo-Soler, F.

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

Cheng, Y.-C.

Y.-C. Cheng and G. R. Fleming, “Coherence quantum beats in two-dimensional electronic spectroscopy,” J. Phys. Chem. A 112(18), 4254–4260 (2008).
[Crossref] [PubMed]

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Chin, A. W.

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

Choi, H. I.

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech 37(6), 862–871 (1989).
[Crossref]

Christensson, N.

N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
[Crossref] [PubMed]

Claasen, T. A. C. M.

T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “Wigner distribution - A tool for time-frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Clafton, S. N.

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

Cohen, L.

L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7(5), 781–786 (1966).
[Crossref]

Collini, E.

E. Collini, “Spectroscopic signatures of quantum-coherent energy transfer,” Chem. Soc. Rev. 42(12), 4932–4947 (2013).
[Crossref] [PubMed]

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

E. Collini and G. D. Scholes, “Coherent intrachain energy migration in a conjugated polymer at room temperature,” Science 323(5912), 369–373 (2009).
[Crossref] [PubMed]

Curmi, P. M. G.

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

Custaud, M.-A.

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Dapang, C.

S. Qian and C. Dapang, “Joint time-frequency analysis,” IEEE Signal Process. Mag. 16(2), 52–67 (1999).
[Crossref]

de Oliveira, P. M.

R. D. Hippenstiel and P. M. de Oliveira, “Time-varying spectral estimation using the instantaneous power spectrum (IPS),” IEEE Trans. Acoust. Speech 38(10), 1752–1759 (1990).
[Crossref]

Du, J.

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

Engel, G. S.

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Ferretti, M.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Fleming, G. R.

Y.-C. Cheng and G. R. Fleming, “Coherence quantum beats in two-dimensional electronic spectroscopy,” J. Phys. Chem. A 112(18), 4254–4260 (2008).
[Crossref] [PubMed]

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Fortrat, J.-O.

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Frutoso, J.

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Fuji, T.

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 332(3-4), 324–330 (2000).
[Crossref]

Gabor, D.

D. Gabor, “Theory of communication,” J. of IEEE 93, 429–457 (1943).

Gharib, C.

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Halpin, A.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Hasegawa, D.

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

Hill, R. N.

H. Margenau and R. N. Hill, “Correlation between measurements in quantum theory,” Prog. Theor. Phys. 26(5), 722–738 (1961).
[Crossref]

Hippenstiel, R. D.

R. D. Hippenstiel and P. M. de Oliveira, “Time-varying spectral estimation using the instantaneous power spectrum (IPS),” IEEE Trans. Acoust. Speech 38(10), 1752–1759 (1990).
[Crossref]

Huelga, S. F.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

S. F. Huelga and M. B. Plenio, “Vibrations, quanta and biology,” Contemp. Phys. 54(4), 181–207 (2013).
[Crossref]

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

Jansen, T. L. C.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Jo Lynn, T.

T. Jo Lynn and A. Z. Bin Sha’ameri, “Signal analysis and classification of digital communication signals using adaptive smooth-windowed Wigner-Ville distribution,” in Proceedings of IEEE Conference on Telecommunication Technologies (IEEE, 2008), pp. 260–266.

Johnson, P. J. M.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Jonas, D. M.

V. Tiwari, W. K. Peters, and D. M. Jonas, “Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework,” Proc. Natl. Acad. Sci. USA 110(4), 1203–1208 (2013).
[Crossref] [PubMed]

Kauffmann, H. F.

N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
[Crossref] [PubMed]

Kee, T. W.

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

Knoester, J.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Kobayashi, T.

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem. Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

A. Yabushita and T. Kobayashi, “Primary conformation change in bacteriorhodopsin on photoexcitation,” Biophys. J. 96(4), 1447–1461 (2009).
[Crossref] [PubMed]

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 332(3-4), 324–330 (2000).
[Crossref]

Kolli, A.

A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
[Crossref] [PubMed]

Liu, T.

X. Wu and T. Liu, “Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution,” J. Appl. Geophys. 68(3), 386–393 (2009).
[Crossref]

Mancal, T.

N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
[Crossref] [PubMed]

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Margenau, H.

H. Margenau and R. N. Hill, “Correlation between measurements in quantum theory,” Prog. Theor. Phys. 26(5), 722–738 (1961).
[Crossref]

Marks, R. J.

Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoust. Speech 38(7), 1084–1091 (1990).
[Crossref]

Mecklenbrauker, W. F. G.

T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “Wigner distribution - A tool for time-frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Miller, R. J. D.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Murphy, R. S.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Nakata, K.

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

Novoderezhkin, V. I.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

O’Reilly, E. J.

A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
[Crossref] [PubMed]

Okamura, K.

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

Olaya-Castro, A.

A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
[Crossref] [PubMed]

Page, C. H.

C. H. Page, “Instantaneous power spectra,” J. Appl. Phys. 23(1), 103–106 (1952).
[Crossref]

Pensack, R. D.

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

Pereira de Souza Neto, E.

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Peters, W. K.

V. Tiwari, W. K. Peters, and D. M. Jonas, “Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework,” Proc. Natl. Acad. Sci. USA 110(4), 1203–1208 (2013).
[Crossref] [PubMed]

Plenio, M. B.

S. F. Huelga and M. B. Plenio, “Vibrations, quanta and biology,” Contemp. Phys. 54(4), 181–207 (2013).
[Crossref]

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

Prior, J.

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

Pullerits, T.

N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
[Crossref] [PubMed]

Qian, S.

S. Qian and C. Dapang, “Joint time-frequency analysis,” IEEE Signal Process. Mag. 16(2), 52–67 (1999).
[Crossref]

Read, E. L.

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

Rihaczek, A. W.

A. W. Rihaczek, “Signal energy distribution in time and frequency,” IEEE Trans. Inf. Theory 14(3), 369–374 (1968).
[Crossref]

Romero, E.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Rosenbach, R.

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

Saito, T.

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 332(3-4), 324–330 (2000).
[Crossref]

Scholes, G. D.

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
[Crossref] [PubMed]

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

E. Collini and G. D. Scholes, “Coherent intrachain energy migration in a conjugated polymer at room temperature,” Science 323(5912), 369–373 (2009).
[Crossref] [PubMed]

Somody, L.

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Song, Y.

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

Stolow, A.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37–R40 (1996).
[Crossref] [PubMed]

Tempelaar, R.

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Thieme, J.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Tiwari, V.

V. Tiwari, W. K. Peters, and D. M. Jonas, “Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework,” Proc. Natl. Acad. Sci. USA 110(4), 1203–1208 (2013).
[Crossref] [PubMed]

Tokunaga, E.

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

van Grondelle, R.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Ville, J.

J. Ville, “Théorie et application de la notion de signal analytique,” Câbles et Transmissions 2eA, 61–74 (1948).

Villeneuve, D. M.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37–R40 (1996).
[Crossref] [PubMed]

Vrakking, M. J. J.

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37–R40 (1996).
[Crossref] [PubMed]

Wigner, E.

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40(5), 749–759 (1932).
[Crossref]

Wilk, K. E.

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

Williams, W. J.

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech 37(6), 862–871 (1989).
[Crossref]

Wong, C. Y.

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

Wu, X.

X. Wu and T. Liu, “Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution,” J. Appl. Geophys. 68(3), 386–393 (2009).
[Crossref]

Yabushita, A.

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem. Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

A. Yabushita and T. Kobayashi, “Primary conformation change in bacteriorhodopsin on photoexcitation,” Biophys. J. 96(4), 1447–1461 (2009).
[Crossref] [PubMed]

Zhao, Y.

Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoust. Speech 38(7), 1084–1091 (1990).
[Crossref]

Zigmantas, D.

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Auton. Neurosci. (1)

E. Pereira de Souza Neto, M.-A. Custaud, J. Frutoso, L. Somody, C. Gharib, and J.-O. Fortrat, “Smoothed pseudo Wigner-Ville distribution as an alternative to Fourier transform in rats,” Auton. Neurosci. 87(2-3), 258–267 (2001).
[Crossref] [PubMed]

Biophys. J. (1)

A. Yabushita and T. Kobayashi, “Primary conformation change in bacteriorhodopsin on photoexcitation,” Biophys. J. 96(4), 1447–1461 (2009).
[Crossref] [PubMed]

Câbles et Transmissions (1)

J. Ville, “Théorie et application de la notion de signal analytique,” Câbles et Transmissions 2eA, 61–74 (1948).

Chem. Phys. Lett. (1)

T. Fuji, T. Saito, and T. Kobayashi, “Dynamical observation of Duschinsky rotation by sub-5-fs real-time spectroscopy,” Chem. Phys. Lett. 332(3-4), 324–330 (2000).
[Crossref]

Chem. Rec. (1)

T. Kobayashi and A. Yabushita, “Transition-state spectroscopy using ultrashort laser pulses,” Chem. Rec. 11(2), 99–116 (2011).
[Crossref] [PubMed]

Chem. Soc. Rev. (1)

E. Collini, “Spectroscopic signatures of quantum-coherent energy transfer,” Chem. Soc. Rev. 42(12), 4932–4947 (2013).
[Crossref] [PubMed]

Contemp. Phys. (1)

S. F. Huelga and M. B. Plenio, “Vibrations, quanta and biology,” Contemp. Phys. 54(4), 181–207 (2013).
[Crossref]

IEEE Signal Process. Mag. (1)

S. Qian and C. Dapang, “Joint time-frequency analysis,” IEEE Signal Process. Mag. 16(2), 52–67 (1999).
[Crossref]

IEEE Trans. Acoust. Speech (3)

H. I. Choi and W. J. Williams, “Improved time-frequency representation of multicomponent signals using exponential kernels,” IEEE Trans. Acoust. Speech 37(6), 862–871 (1989).
[Crossref]

R. D. Hippenstiel and P. M. de Oliveira, “Time-varying spectral estimation using the instantaneous power spectrum (IPS),” IEEE Trans. Acoust. Speech 38(10), 1752–1759 (1990).
[Crossref]

Y. Zhao, L. E. Atlas, and R. J. Marks, “The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals,” IEEE Trans. Acoust. Speech 38(7), 1084–1091 (1990).
[Crossref]

IEEE Trans. Inf. Theory (1)

A. W. Rihaczek, “Signal energy distribution in time and frequency,” IEEE Trans. Inf. Theory 14(3), 369–374 (1968).
[Crossref]

J. Appl. Geophys. (1)

X. Wu and T. Liu, “Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution,” J. Appl. Geophys. 68(3), 386–393 (2009).
[Crossref]

J. Appl. Phys. (1)

C. H. Page, “Instantaneous power spectra,” J. Appl. Phys. 23(1), 103–106 (1952).
[Crossref]

J. Chem. Phys. (2)

J. Prior, E. Castro, A. W. Chin, J. Almeida, S. F. Huelga, and M. B. Plenio, “Wavelet analysis of molecular dynamics: efficient extraction of time-frequency information in ultrafast optical processes,” J. Chem. Phys. 139(22), 224103 (2013).
[Crossref] [PubMed]

A. Kolli, E. J. O’Reilly, G. D. Scholes, and A. Olaya-Castro, “The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae,” J. Chem. Phys. 137(17), 174109 (2012).
[Crossref] [PubMed]

J. Math. Phys. (1)

L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys. 7(5), 781–786 (1966).
[Crossref]

J. of IEEE (1)

D. Gabor, “Theory of communication,” J. of IEEE 93, 429–457 (1943).

J. Phys. Chem. A (2)

D. Hasegawa, K. Nakata, E. Tokunaga, K. Okamura, J. Du, and T. Kobayashi, “Vibrational energy flow between modes by dynamic mode coupling in THIATS J-aggregates,” J. Phys. Chem. A 117(45), 11441–11448 (2013).
[Crossref] [PubMed]

Y.-C. Cheng and G. R. Fleming, “Coherence quantum beats in two-dimensional electronic spectroscopy,” J. Phys. Chem. A 112(18), 4254–4260 (2008).
[Crossref] [PubMed]

J. Phys. Chem. B (1)

N. Christensson, H. F. Kauffmann, T. Pullerits, and T. Mančal, “Origin of long-lived coherences in light-harvesting complexes,” J. Phys. Chem. B 116(25), 7449–7454 (2012).
[Crossref] [PubMed]

Nat. Chem. (1)

A. Halpin, P. J. M. Johnson, R. Tempelaar, R. S. Murphy, J. Knoester, T. L. C. Jansen, and R. J. D. Miller, “Two-dimensional spectroscopy of a molecular dimer unveils the effects of vibronic coupling on exciton coherences,” Nat. Chem. 6(3), 196–201 (2014).
[Crossref] [PubMed]

Nat. Commun. (1)

Y. Song, S. N. Clafton, R. D. Pensack, T. W. Kee, and G. D. Scholes, “Vibrational coherence probes the mechanism of ultrafast electron transfer in polymer-fullerene blends,” Nat. Commun. 5, 4933 (2014).
[Crossref] [PubMed]

Nat. Phys. (2)

A. W. Chin, J. Prior, R. Rosenbach, F. Caycedo-Soler, S. F. Huelga, and M. B. Plenio, “The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment-protein complexes,” Nat. Phys. 9(2), 113–118 (2013).
[Crossref]

E. Romero, R. Augulis, V. I. Novoderezhkin, M. Ferretti, J. Thieme, D. Zigmantas, and R. van Grondelle, “Quantum coherence in photosynthesis for efficient solar-energy conversion,” Nat. Phys. 10(9), 676–682 (2014).
[Crossref]

Nature (2)

G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mancal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature 446(7137), 782–786 (2007).
[Crossref] [PubMed]

E. Collini, C. Y. Wong, K. E. Wilk, P. M. G. Curmi, P. Brumer, and G. D. Scholes, “Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature,” Nature 463(7281), 644–647 (2010).
[Crossref] [PubMed]

Philips J. Res. (1)

T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “Wigner distribution - A tool for time-frequency signal analysis,” Philips J. Res. 35, 217–250 (1980).

Phys. Rev. (1)

E. Wigner, “On the quantum correction for thermodynamic equilibrium,” Phys. Rev. 40(5), 749–759 (1932).
[Crossref]

Phys. Rev. A (1)

M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, “Observation of fractional revivals of a molecular wave packet,” Phys. Rev. A 54(1), R37–R40 (1996).
[Crossref] [PubMed]

Proc. IEEE (1)

L. Cohen, “Time-frequency distributions-a review,” Proc. IEEE 77(7), 941–981 (1989).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

V. Tiwari, W. K. Peters, and D. M. Jonas, “Electronic resonance with anticorrelated pigment vibrations drives photosynthetic energy transfer outside the adiabatic framework,” Proc. Natl. Acad. Sci. USA 110(4), 1203–1208 (2013).
[Crossref] [PubMed]

Prog. Theor. Phys. (1)

H. Margenau and R. N. Hill, “Correlation between measurements in quantum theory,” Prog. Theor. Phys. 26(5), 722–738 (1961).
[Crossref]

Science (1)

E. Collini and G. D. Scholes, “Coherent intrachain energy migration in a conjugated polymer at room temperature,” Science 323(5912), 369–373 (2009).
[Crossref] [PubMed]

Other (5)

S. Mukamel, Principles of Nonlinear Optics and Spectroscopy (Oxford University, 1995).

K. Gröchenig, Foundations of Time-Frequency Analysis (Springer Science, 2001).

T. Jo Lynn and A. Z. Bin Sha’ameri, “Signal analysis and classification of digital communication signals using adaptive smooth-windowed Wigner-Ville distribution,” in Proceedings of IEEE Conference on Telecommunication Technologies (IEEE, 2008), pp. 260–266.

S. M. Kay, Modern Spectral Estimation: Theory and Application (Prentice Hall, 1988).

S. L. Marple, Digital Spectral Analysis: With Applications (Prentice Hall, 1987).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 (a) Pictorial representation of the 3D data set typically obtained with a 2DES experiment; the evolution of a 2D frequency-frequency map is measured along the delay time T. (b) The decay of the signal can be extracted at a given coordinate on the frequency-frequency map as a function of the delay time T. The obtained oscillating trace has the same typical behavior of oscillating signals obtained through other ultrafast coherent spectroscopies. (c) Fourier Transform of the oscillating residuals highlighting the frequency components contributing to the beating. The data in panels (b) and (c) refer to sample measurements performed on HITCI dye solutions.
Fig. 2
Fig. 2 Representation of the time-frequency plane. The 2D plot shows an example of a time-frequency map displaying the amplitude of signals at different frequencies over time, making it possible to track changes in amplitudes over a given time span. The originating signal is shown for comparison in the frequency and time domain on the left and on top, respectively.
Fig. 3
Fig. 3 Time-frequency plots showing the results of the analysis performed by STFT with Gaussian windows of increasing width from left to right. The original signal in the frequency and time domain is shown for comparison on the left and on top of the panels, respectively. The time resolution worsens from left to right.
Fig. 4
Fig. 4 Comparison between (a) Wigner-Ville [WV], (b) pseudo-Wigner-Ville [PWV] and (c) smoothed-pseudo-Wigner-Ville [SPWV] transforms. The original signal in the frequency and time domain is shown for comparison on the left and on top of the panels, respectively. Cross-term interference artifacts appearing between relevant signals along the time and frequency axes are highlighted by red lines. The introduction of the first window h removes interference between signals not superimposed in time. The second window g performs a smoothing in time, removing the residual interferences. The final SPWV does not present cross-terms contaminations but the resolution is clearly lowered.
Fig. 5
Fig. 5 Comparison of the results obtained applying different TFT analysis to a multicomponent signal mimicking experimental data. (a) Analyzed signal in the time and frequency domain. In this specific case: v1 = 200cm−1; v2 = 375cm−1; v3 = 800cm−1; t1 = 2ps; t2 = 200fs ; t3 = 500fs; A1 = A2 = A3 = 1; (b) Scalogram (|CWT|2), obtained with a gaussian Morlet window ψ= (1 / σ b 2π ) exp (t/2 σ b ) 2 exp(i2π f c t) with σb = 0.7 and fc = 1; (c) Spectrogram, (|STFT|2), Gaussian window h(t)=(1/ σ h 2π )exp( t 2 /4 σ h ) σh = 100 fs; (d) Margenau-Hill spectrogram (MHS), σh = 55 fs and σg = 150 fs; (e) Smoothed-pseudo-Wigner-Ville (SPWV), σh = σg = 75 fs; and (f) Smoothed Choi-Williams (SCW), σh = σg = 80 fs, α = 0.1.
Fig. 6
Fig. 6 Effect of the noise on TFT performances. (a) Analyzed signal in the time and frequency domain. In this specific case: v1 = 200cm−1; v2 = 375cm−1; v3 = 800cm−1; t1 = 2ps; t2 = 200fs; t3 = 500fs; noise level k = 0.5. (b) Scalogram (|CWT|2); (c) Spectrogram (|STFT|2); (d) Margenau-Hill spectrogram (MHS); (e) Smoothed-pseudo-Wigner-Ville (SPWV); and (f) Smoothed Choi-Williams (SCW). Window parameters as in Fig. 5.
Fig. 7
Fig. 7 (a) Windows functions tested in the TFT analysis. From the bottom to the top: top-hat, Bartlett, Gaussian, Blackman, and Hanning function. The windows have been normalized by area. (b-f) Results obtained applying the Short Time Fourier Transform (STFT) for the analysis of the signal of Fig. 5 using (b) the top-hat window function; (c) the Bartlett window function; (d) the Gaussian window function; (e) the Blackman window function, and (f) the Hanning window function.

Equations (9)

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

S(ν)=FT{ s(t) }= + s(t) e i2πνt dt
STFT(t,ν)= + s(t') h * (t't) e i2πνt' dt
CWT(t,a)= 1 | a | + s(t') ψ * ( t't a ) dt
MHS(t,ν)=Re{ STF T h (t,v)STF T g * (t,v) }
WV(t,v)= + dt's( t+ t' 2 ) s * ( t t' 2 ) e i2πvt'
SPWV(t,v)= + h(t') + g(t''t) s( t''+ t' 2 ) s * ( t'' t' 2 ) e i2πvt' dt'dt''
CW(t,v)= + α 4π | t'' | exp( t ' 2 α (4t'') 2 )s( t+t'+ t'' 2 ) s * ( t+t' t'' 2 ) e i2πvt' dt'dt''
SCW(t,v)= + h(t'') + g(t') α 4π | t'' | exp( (t') 2 α (4t'') 2 )s( t+t'+ t'' 2 ) s * ( t+t' t'' 2 ) e i2πvt'' dt'dt''
y(t,v)= n=1 3 A n exp(t/ t n )cos(2π v n t)

Metrics