Abstract

To investigate the perception of a temporal envelope of flickering light is important for understanding nonlinear temporal processing in the visual system. The influence of the frequency components of a flickering light on the perception of the envelope remains unclear, with few studies having investigated the cortical activities for the envelope. We investigated the detection thresholds, brightness, and magnetoencephalographic responses related to amplitude-modulated (AM) flickering lights. The results showed that the sensitivity to flicker at the envelope periodicity of the AM flickering light was lower for a high-frequency carrier (40 Hz) than for a lower-frequency one (10, 20, or 30 Hz). Also, the primary visual cortex responded at the frequency corresponding to the envelope periodicity of the AM flickering light, and the strength of the cortical response reflected the brightness of the flicker at the envelope periodicity.

© 2009 Optical Society of America

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2006 (1)

V. Zemon and J. Gordon, “Luminance-contrast mechanisms in humans: visual evoked potentials and a nonlinear model,” Vision Res. 46, 4163-4180 (2006).
[CrossRef] [PubMed]

2004 (1)

I. P. Fawcett, G. R. Barnes, A. Hillebrand, and K. D. Singh, “The temporal frequency tuning of human visual cortex investigated using synthetic aperture magnetometry,” Neuroimage 21, 1542-1553 (2004).
[CrossRef] [PubMed]

2001 (1)

C. S. Herrmann, “Human EEG responses to 1-100 Hz flicker: resonance phenomena in visual cortex and their potential correlation to cognitive phenomena,” Exp. Brain Res. 137, 346-353 (2001).
[CrossRef] [PubMed]

2000 (4)

K. D. Singh, A. T. Smith, and M. W. Greenlee, “Spatiotemporal frequency and direction sensitivities of human visual areas measured using fMRI,” Neuroimage 12, 550-564 (2000).
[CrossRef] [PubMed]

K. Fujii, S. Kita, T. Matsushima, and Y. Ando, “The missing fundamental phenomenon in the temporal vision,” Psychol. Res. 64, 149-154 (2000).
[CrossRef]

A. Gorea, C. Wardak, and C. Lorenzi, “Visual sensitivity to temporal modulations of temporal noise,” Vision Res. 40, 3817-3822 (2000).
[CrossRef] [PubMed]

A. Kohlrausch, R. Fassel, and T. Dau, “The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers,” J. Acoust. Soc. Am. 108, 723-734 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Rovamo, A. Raninen, and K. Donner, “The effects of temporal noise and retinal illuminance on foveal flicker sensitivity,” Vision Res. 39, 533-550 (1999).
[CrossRef] [PubMed]

1998 (3)

A. Stockman and J. Plummer, “Color from invisible flicker: a failure of the Talbot-Plateau law caused by an early 'hard' saturating nonlinearity used to partition the human short-wave cone pathway,” Vision Res. 38, 3703-3728 (1998).
[CrossRef]

C. G. Thomas and R. S. Menon, “Amplitude response and stimulus presentation frequency response of human primary visual cortex using BOLD EPI at 4 T,” Magn. Reson. Med. 40, 203-209 (1998).
[CrossRef] [PubMed]

M. A. García-Pérez, “Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties,” Vision Res. 38, 1861-1881 (1998).
[CrossRef] [PubMed]

1997 (1)

F. Fylan, I. E. Holliday, K. D. Singh, S. J. Anderson, and G. F. A. Harding, “Magnetoencephalographic investigation of human cortical area V1 using color stimuli,” Neuroimage 6, 47-57 (1997).
[CrossRef] [PubMed]

1996 (4)

J. Rovamo, A. Raninen, S. Lukkarinen, and K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767-3774 (1996).
[CrossRef] [PubMed]

S. Wu, S. A. Burns, A. Reeves, and A. E. Elsner, “Flicker brightness enhancement and visual nonlinearity,” Vision Res. 36, 1573-1583 (1996).
[CrossRef] [PubMed]

M. C. Morrone, A. Fiorentini, and D. C. Burr, “Development of the temporal properties of visual evoked potentials to luminance and colour contrast in infants,” Vision Res. 36, 3141-3155 (1996).
[CrossRef] [PubMed]

S. A. Burns and A. E. Elsner, “Response of retina at low temporal frequencies,” J. Opt. Soc. Am. A 13, 667-672 (1996).
[CrossRef]

1994 (1)

S. T. Hammett and A. T. Smith, “Temporal beats in the human visual system,” Vision Res. 34, 2833-2840 (1994).
[CrossRef] [PubMed]

1992 (1)

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

1991 (1)

A. Stockman, D. I. A. MacLeod, and D. D. DePriest, “The temporal properties of the human short-wave photoreceptors and their associated pathways,” Vision Res. 31, 189-208 (1991).
[CrossRef] [PubMed]

1988 (1)

L. W. Baitch and D. M. Levi, “Evidence for nonlinear binocular interactions in human visual cortex,” Vision Res. 28, 1139-1143 (1988).
[CrossRef] [PubMed]

1984 (1)

P. T. Fox and M. E. Raichle, “Stumulus rate dependence of regional cerebral blood flow in human striate cortex,” J. Neurophysiol. 51, 1109-1120 (1984).
[PubMed]

1973 (1)

1971 (1)

1961 (1)

1958 (1)

Anderson, S. J.

F. Fylan, I. E. Holliday, K. D. Singh, S. J. Anderson, and G. F. A. Harding, “Magnetoencephalographic investigation of human cortical area V1 using color stimuli,” Neuroimage 6, 47-57 (1997).
[CrossRef] [PubMed]

Ando, Y.

K. Fujii, S. Kita, T. Matsushima, and Y. Ando, “The missing fundamental phenomenon in the temporal vision,” Psychol. Res. 64, 149-154 (2000).
[CrossRef]

Baitch, L. W.

L. W. Baitch and D. M. Levi, “Evidence for nonlinear binocular interactions in human visual cortex,” Vision Res. 28, 1139-1143 (1988).
[CrossRef] [PubMed]

Barnes, G. R.

I. P. Fawcett, G. R. Barnes, A. Hillebrand, and K. D. Singh, “The temporal frequency tuning of human visual cortex investigated using synthetic aperture magnetometry,” Neuroimage 21, 1542-1553 (2004).
[CrossRef] [PubMed]

Bartley, S. H.

S. H. Bartley, “A clarification of some of the procedures and concepts involved in dealing with the optic pathway,” in Symposium on the Visual System: Neurophysiology and Psychophysics, R.Jung and H.Kornhuber, eds. (Springer, 1961).

Belliveau, J. W.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Bornstein, M. H.

Burns, S. A.

S. Wu, S. A. Burns, A. Reeves, and A. E. Elsner, “Flicker brightness enhancement and visual nonlinearity,” Vision Res. 36, 1573-1583 (1996).
[CrossRef] [PubMed]

S. A. Burns and A. E. Elsner, “Response of retina at low temporal frequencies,” J. Opt. Soc. Am. A 13, 667-672 (1996).
[CrossRef]

Burr, D. C.

M. C. Morrone, A. Fiorentini, and D. C. Burr, “Development of the temporal properties of visual evoked potentials to luminance and colour contrast in infants,” Vision Res. 36, 3141-3155 (1996).
[CrossRef] [PubMed]

Chesler, D. A.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Cohen, M. S.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Dau, T.

A. Kohlrausch, R. Fassel, and T. Dau, “The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers,” J. Acoust. Soc. Am. 108, 723-734 (2000).
[CrossRef] [PubMed]

DeLange, H.

DePriest, D. D.

A. Stockman, D. I. A. MacLeod, and D. D. DePriest, “The temporal properties of the human short-wave photoreceptors and their associated pathways,” Vision Res. 31, 189-208 (1991).
[CrossRef] [PubMed]

Donner, K.

J. Rovamo, A. Raninen, and K. Donner, “The effects of temporal noise and retinal illuminance on foveal flicker sensitivity,” Vision Res. 39, 533-550 (1999).
[CrossRef] [PubMed]

J. Rovamo, A. Raninen, S. Lukkarinen, and K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767-3774 (1996).
[CrossRef] [PubMed]

Elsner, A. E.

S. A. Burns and A. E. Elsner, “Response of retina at low temporal frequencies,” J. Opt. Soc. Am. A 13, 667-672 (1996).
[CrossRef]

S. Wu, S. A. Burns, A. Reeves, and A. E. Elsner, “Flicker brightness enhancement and visual nonlinearity,” Vision Res. 36, 1573-1583 (1996).
[CrossRef] [PubMed]

Fassel, R.

A. Kohlrausch, R. Fassel, and T. Dau, “The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers,” J. Acoust. Soc. Am. 108, 723-734 (2000).
[CrossRef] [PubMed]

Fawcett, I. P.

I. P. Fawcett, G. R. Barnes, A. Hillebrand, and K. D. Singh, “The temporal frequency tuning of human visual cortex investigated using synthetic aperture magnetometry,” Neuroimage 21, 1542-1553 (2004).
[CrossRef] [PubMed]

Fiorentini, A.

M. C. Morrone, A. Fiorentini, and D. C. Burr, “Development of the temporal properties of visual evoked potentials to luminance and colour contrast in infants,” Vision Res. 36, 3141-3155 (1996).
[CrossRef] [PubMed]

Fox, P. T.

P. T. Fox and M. E. Raichle, “Stumulus rate dependence of regional cerebral blood flow in human striate cortex,” J. Neurophysiol. 51, 1109-1120 (1984).
[PubMed]

Fujii, K.

K. Fujii, S. Kita, T. Matsushima, and Y. Ando, “The missing fundamental phenomenon in the temporal vision,” Psychol. Res. 64, 149-154 (2000).
[CrossRef]

Fylan, F.

F. Fylan, I. E. Holliday, K. D. Singh, S. J. Anderson, and G. F. A. Harding, “Magnetoencephalographic investigation of human cortical area V1 using color stimuli,” Neuroimage 6, 47-57 (1997).
[CrossRef] [PubMed]

García-Pérez, M. A.

M. A. García-Pérez, “Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties,” Vision Res. 38, 1861-1881 (1998).
[CrossRef] [PubMed]

Goldberg, I. E.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Gordon, J.

V. Zemon and J. Gordon, “Luminance-contrast mechanisms in humans: visual evoked potentials and a nonlinear model,” Vision Res. 46, 4163-4180 (2006).
[CrossRef] [PubMed]

Gorea, A.

A. Gorea, C. Wardak, and C. Lorenzi, “Visual sensitivity to temporal modulations of temporal noise,” Vision Res. 40, 3817-3822 (2000).
[CrossRef] [PubMed]

Greenlee, M. W.

K. D. Singh, A. T. Smith, and M. W. Greenlee, “Spatiotemporal frequency and direction sensitivities of human visual areas measured using fMRI,” Neuroimage 12, 550-564 (2000).
[CrossRef] [PubMed]

Hammett, S. T.

S. T. Hammett and A. T. Smith, “Temporal beats in the human visual system,” Vision Res. 34, 2833-2840 (1994).
[CrossRef] [PubMed]

Harding, G. F. A.

F. Fylan, I. E. Holliday, K. D. Singh, S. J. Anderson, and G. F. A. Harding, “Magnetoencephalographic investigation of human cortical area V1 using color stimuli,” Neuroimage 6, 47-57 (1997).
[CrossRef] [PubMed]

Herrmann, C. S.

C. S. Herrmann, “Human EEG responses to 1-100 Hz flicker: resonance phenomena in visual cortex and their potential correlation to cognitive phenomena,” Exp. Brain Res. 137, 346-353 (2001).
[CrossRef] [PubMed]

Hillebrand, A.

I. P. Fawcett, G. R. Barnes, A. Hillebrand, and K. D. Singh, “The temporal frequency tuning of human visual cortex investigated using synthetic aperture magnetometry,” Neuroimage 21, 1542-1553 (2004).
[CrossRef] [PubMed]

Holliday, I. E.

F. Fylan, I. E. Holliday, K. D. Singh, S. J. Anderson, and G. F. A. Harding, “Magnetoencephalographic investigation of human cortical area V1 using color stimuli,” Neuroimage 6, 47-57 (1997).
[CrossRef] [PubMed]

Hoppel, B. E.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Kelly, D. H.

Kennedy, D. N.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Kita, S.

K. Fujii, S. Kita, T. Matsushima, and Y. Ando, “The missing fundamental phenomenon in the temporal vision,” Psychol. Res. 64, 149-154 (2000).
[CrossRef]

Kohlrausch, A.

A. Kohlrausch, R. Fassel, and T. Dau, “The influence of carrier level and frequency on modulation and beat-detection thresholds for sinusoidal carriers,” J. Acoust. Soc. Am. 108, 723-734 (2000).
[CrossRef] [PubMed]

Kwong, K. K.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Levi, D. M.

L. W. Baitch and D. M. Levi, “Evidence for nonlinear binocular interactions in human visual cortex,” Vision Res. 28, 1139-1143 (1988).
[CrossRef] [PubMed]

Lorenzi, C.

A. Gorea, C. Wardak, and C. Lorenzi, “Visual sensitivity to temporal modulations of temporal noise,” Vision Res. 40, 3817-3822 (2000).
[CrossRef] [PubMed]

Lukkarinen, S.

J. Rovamo, A. Raninen, S. Lukkarinen, and K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767-3774 (1996).
[CrossRef] [PubMed]

MacLeod, D. I. A.

A. Stockman, D. I. A. MacLeod, and D. D. DePriest, “The temporal properties of the human short-wave photoreceptors and their associated pathways,” Vision Res. 31, 189-208 (1991).
[CrossRef] [PubMed]

Marks, E.

Matsushima, T.

K. Fujii, S. Kita, T. Matsushima, and Y. Ando, “The missing fundamental phenomenon in the temporal vision,” Psychol. Res. 64, 149-154 (2000).
[CrossRef]

Menon, R. S.

C. G. Thomas and R. S. Menon, “Amplitude response and stimulus presentation frequency response of human primary visual cortex using BOLD EPI at 4 T,” Magn. Reson. Med. 40, 203-209 (1998).
[CrossRef] [PubMed]

Morrone, M. C.

M. C. Morrone, A. Fiorentini, and D. C. Burr, “Development of the temporal properties of visual evoked potentials to luminance and colour contrast in infants,” Vision Res. 36, 3141-3155 (1996).
[CrossRef] [PubMed]

Plummer, J.

A. Stockman and J. Plummer, “Color from invisible flicker: a failure of the Talbot-Plateau law caused by an early 'hard' saturating nonlinearity used to partition the human short-wave cone pathway,” Vision Res. 38, 3703-3728 (1998).
[CrossRef]

Poncelet, B. P.

K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen, and R. Turner, “Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation,” Proc. Natl. Acad. Sci. U.S.A. 89, 5675-5679 (1992).
[CrossRef] [PubMed]

Raichle, M. E.

P. T. Fox and M. E. Raichle, “Stumulus rate dependence of regional cerebral blood flow in human striate cortex,” J. Neurophysiol. 51, 1109-1120 (1984).
[PubMed]

Raninen, A.

J. Rovamo, A. Raninen, and K. Donner, “The effects of temporal noise and retinal illuminance on foveal flicker sensitivity,” Vision Res. 39, 533-550 (1999).
[CrossRef] [PubMed]

J. Rovamo, A. Raninen, S. Lukkarinen, and K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767-3774 (1996).
[CrossRef] [PubMed]

Reeves, A.

S. Wu, S. A. Burns, A. Reeves, and A. E. Elsner, “Flicker brightness enhancement and visual nonlinearity,” Vision Res. 36, 1573-1583 (1996).
[CrossRef] [PubMed]

Regan, D.

D. Regan, Human Brain Electrophysiology: Evoked Potentials and Evoked Magnetic Fields in Science and Medicine (Elsevier, 1989).
[PubMed]

Rovamo, J.

J. Rovamo, A. Raninen, and K. Donner, “The effects of temporal noise and retinal illuminance on foveal flicker sensitivity,” Vision Res. 39, 533-550 (1999).
[CrossRef] [PubMed]

J. Rovamo, A. Raninen, S. Lukkarinen, and K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767-3774 (1996).
[CrossRef] [PubMed]

Silberstein, R. B.

R. B. Silberstein, “Steady-state visually evoked potentials, brain resonances, and cognitive processes,” in Neocortical Dynamics and Human EEG Rhythms, P.L.Nunez, ed. (Oxford Univ. Press, 1995), pp. 272-303.

Singh, K. D.

I. P. Fawcett, G. R. Barnes, A. Hillebrand, and K. D. Singh, “The temporal frequency tuning of human visual cortex investigated using synthetic aperture magnetometry,” Neuroimage 21, 1542-1553 (2004).
[CrossRef] [PubMed]

K. D. Singh, A. T. Smith, and M. W. Greenlee, “Spatiotemporal frequency and direction sensitivities of human visual areas measured using fMRI,” Neuroimage 12, 550-564 (2000).
[CrossRef] [PubMed]

F. Fylan, I. E. Holliday, K. D. Singh, S. J. Anderson, and G. F. A. Harding, “Magnetoencephalographic investigation of human cortical area V1 using color stimuli,” Neuroimage 6, 47-57 (1997).
[CrossRef] [PubMed]

Smith, A. T.

K. D. Singh, A. T. Smith, and M. W. Greenlee, “Spatiotemporal frequency and direction sensitivities of human visual areas measured using fMRI,” Neuroimage 12, 550-564 (2000).
[CrossRef] [PubMed]

S. T. Hammett and A. T. Smith, “Temporal beats in the human visual system,” Vision Res. 34, 2833-2840 (1994).
[CrossRef] [PubMed]

Stockman, A.

A. Stockman and J. Plummer, “Color from invisible flicker: a failure of the Talbot-Plateau law caused by an early 'hard' saturating nonlinearity used to partition the human short-wave cone pathway,” Vision Res. 38, 3703-3728 (1998).
[CrossRef]

A. Stockman, D. I. A. MacLeod, and D. D. DePriest, “The temporal properties of the human short-wave photoreceptors and their associated pathways,” Vision Res. 31, 189-208 (1991).
[CrossRef] [PubMed]

Thomas, C. G.

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Figures (6)

Fig. 1
Fig. 1

Examples of waveforms (first 2 s) and amplitude spectra of an AM flickering light with a modulation frequency of 2 Hz. Left, AM flickering light with a carrier frequency of 10 Hz and a modulation depth of 1.0; right, light with a carrier frequency of 40 Hz and a modulation depth of 0.1.

Fig. 2
Fig. 2

Thresholds for detecting the modulation frequencies of AM flickering lights averaged over all subjects. Different symbols indicate different modulation frequencies. Error bars indicate standard error of the mean (SEM) ( p * * < 0.01 ) .

Fig. 3
Fig. 3

Brightness-matching data averaged over all subjects. The abscissa represents the carrier frequency of the AM flickering light. The ordinate represents the modulation depth of a sinusoidal flickering light to match the brightness of the flicker at the modulation frequency of the AM flickering light. Error bars indicate SEM ( p * < 0.05 , p * * < 0.01 ) .

Fig. 4
Fig. 4

(a) Example of a MEG signal for the AM flickering light. The signal was obtained from one MEG sensor over the occipital area during stimulation (30 s) for a single participant. A 2 s signal filtered with a bandpass of 1–25 Hz is shown for the display. The modulation and carrier frequencies of AM flickering light were 4 and 20 Hz, respectively. (b) Power spectrum of the 30 s MEG signal. (c) An example of the distribution of MEG responses at the modulation frequency, gathered from three participants for an AM flickering light with a modulator of 4 Hz, a carrier of 20 Hz, and a modulation depth of 1.

Fig. 5
Fig. 5

Power of MEG signals at the modulation frequencies of AM flickering lights. Modulation frequencies are (a) 1, (b) 2 and (c) 4 Hz. Different symbols indicate different modulation depths. Error bars indicate SEM ( p * < 0.05 , p * * < 0.01 ) .

Fig. 6
Fig. 6

Power of the MEG signals at the carrier frequencies of AM flickering lights with modulation frequencies of 1, 2, and 4 Hz. Different symbols indicate different modulation depths. Error bars indicate SEM ( p * * < 0.01 ) .

Tables (1)

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Table 1 Results of Two-Way ANOVAs for Power of MEG Signals

Equations (1)

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L ( t ) = L 0 + 0.5 L 0 [ 1 + m sin ( 2 π f m t + 1.5 π ) ] sin 2 π f c t ,

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