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Wigner (time-frequency) distributions of averaged event-related potentials
$238 Differentiation has also been achieved by plotting phase angle against trial number. These findings are also described.
DPP2.09 W1GNER (TIME-FREQUENCY) D I S T R I B U T I O N S O F AVERAGED EVENT-RELATED P O T E N T I A L S . A.S. Gevins and N.H. Morgan
(San Francisco, CA, USA) The event related potential (ERP) waveform is a funtion of time and does not provide explicit frequency information. Power spectra of ERP waveforms provide frequency information but obscure time-dependent phenomena. A view of the spectrum as it changed over time would give a new view of the evolution of different frequency components of the ERP. Simple approaches, such as computing the spectrum over highly overlapped segments of the average ERP, are unsuitable since discrete temporal events are still smeared together within each analysis window. While there is an unavoidable trade-off between frequency and time resoluton, the spectrogram is an inflexible way of determining this choice. A preferred method is to compute a function of time and frequency without fixed resolution trade-offs. The Wigner Distribution is a function which approximates the instantaneous energy for a given time and frequency; it gives a raw 'distribution' which can be averaged over many different time and frequency regions to give valid energy estimates. The Wigner Distribution has been applied to several types of stimulus- and response-registered ERPS, revealing that conventional ERP peaks, such as N100, P200, P300, etc. consist of processes which change rapidly in both time and frequency. Distinct energy 'peaks' are seen in the Wigner Distribution, allowing very simple interpretations of the time and frequency locations of signal energy.
DPP2.10 M E A S U R E S POTENTIALS.
OF VARIABILITY O F
EVOKED
R. Cooper, P.V. Pocock and S.H. Curry
(Bristol, UK) Determination of base line against which amplitude measures of evoked potential components can be taken has always been a difficult problem especially when recording slowly changing activity (CNV or Bereitschaftspotential for example). The usual method is to 'normalise' by subtracting an average value of a particular period of pre-stimulus activity from the subsequent data. However, if measures of point to point variability are required across all trials entered into an average (standard deviations for example), then each trial must be entered into the variability calculation before normalisation is done since the normalisation will artificially reduce the measure of variability at the beginning of the trial.
Similarly the entry of sets of averaged evoked potentials into analytic procedures must be done with care especially if the procedures depend upon the variability across cases e.g. conditions, electrodes etc. (as distinct from the trial to trial variability above) as in principal component analysis. Artificial 'components' can be extracted and others distorted because of variability from non-physiological sources (e.g. channel offset) if cases are not normalised. However, the period used for this normalisation must be chosen carefully as sections of data with artificially reduced variability will also affect the resulting factor structure.
DPP2.11 P R I N C I P A L C O M P O N E N T ANALYSIS OF ERPS: F U R T H E R S I M U L A T I O N STUDIES. C.C. Wood and G. McCarthy
(West Haven, CT, USA) Event-related potentials (ERPs) pose difficult analytic problems because of inherent statistical dependencies between data values at different time points and because each value is often the result of overlapping influences. Principal Component Analysis (PCA), a multivariate statistical procedure closely related to factor analysis, has become a widely accepted means of dealing with these problems. Because the true component structure of the ERP data typically analyzed by PCA is unknown, Wood and McCarthy (Electroenceph. clin. Neurophysiol., 1984, 59: 249) used simulated ERP components to investigate the ability of PCA, Varimax rotation, and univariate A N O V A s to reconstruct component wave shapes, to allocate variance correctly across components, and to identify the correct locus of experimental effects. Under the near-optimal conditions employed, PCA reconstructed the wave shapes of the simulated components reasonably well; however, variance was incorrectly al'located across overlapping components, producing dramatic increases in Type l error for ANOVAs on one component when the true treatment effect was on another. Here we extend these results to simulated components with different scalp distributions; such differences are thought to facilitate accurate component extraction by PCA. Large increases in Type 1 error were again obtained, indicating that differences in scalp distribution do not eliminate variance misallocation by PCA.
DPP2.12 T E M P O R A l , R E L A T I O N S H I P OF S U B J E C T I V E P E R C E P T I O N AND T H E N E U R O N A L EVENTS IND U C E D BY P E R I P H E R A L S T I M U L A T I O N . W. Massing
(Langenhagen, W. Germany) Libet et al. stimulated the cortex of h u m a n subjects during the course of surgical treatment and found that perception of the
DPP2.09 W1GNER (TIME-FREQUENCY) D I S T R I B U T I O N S O F AVERAGED EVENT-RELATED P O T E N T I A L S . A.S. Gevins and N.H. Morgan
(San Francisco, CA, USA) The event related potential (ERP) waveform is a funtion of time and does not provide explicit frequency information. Power spectra of ERP waveforms provide frequency information but obscure time-dependent phenomena. A view of the spectrum as it changed over time would give a new view of the evolution of different frequency components of the ERP. Simple approaches, such as computing the spectrum over highly overlapped segments of the average ERP, are unsuitable since discrete temporal events are still smeared together within each analysis window. While there is an unavoidable trade-off between frequency and time resoluton, the spectrogram is an inflexible way of determining this choice. A preferred method is to compute a function of time and frequency without fixed resolution trade-offs. The Wigner Distribution is a function which approximates the instantaneous energy for a given time and frequency; it gives a raw 'distribution' which can be averaged over many different time and frequency regions to give valid energy estimates. The Wigner Distribution has been applied to several types of stimulus- and response-registered ERPS, revealing that conventional ERP peaks, such as N100, P200, P300, etc. consist of processes which change rapidly in both time and frequency. Distinct energy 'peaks' are seen in the Wigner Distribution, allowing very simple interpretations of the time and frequency locations of signal energy.
DPP2.10 M E A S U R E S POTENTIALS.
OF VARIABILITY O F
EVOKED
R. Cooper, P.V. Pocock and S.H. Curry
(Bristol, UK) Determination of base line against which amplitude measures of evoked potential components can be taken has always been a difficult problem especially when recording slowly changing activity (CNV or Bereitschaftspotential for example). The usual method is to 'normalise' by subtracting an average value of a particular period of pre-stimulus activity from the subsequent data. However, if measures of point to point variability are required across all trials entered into an average (standard deviations for example), then each trial must be entered into the variability calculation before normalisation is done since the normalisation will artificially reduce the measure of variability at the beginning of the trial.
Similarly the entry of sets of averaged evoked potentials into analytic procedures must be done with care especially if the procedures depend upon the variability across cases e.g. conditions, electrodes etc. (as distinct from the trial to trial variability above) as in principal component analysis. Artificial 'components' can be extracted and others distorted because of variability from non-physiological sources (e.g. channel offset) if cases are not normalised. However, the period used for this normalisation must be chosen carefully as sections of data with artificially reduced variability will also affect the resulting factor structure.
DPP2.11 P R I N C I P A L C O M P O N E N T ANALYSIS OF ERPS: F U R T H E R S I M U L A T I O N STUDIES. C.C. Wood and G. McCarthy
(West Haven, CT, USA) Event-related potentials (ERPs) pose difficult analytic problems because of inherent statistical dependencies between data values at different time points and because each value is often the result of overlapping influences. Principal Component Analysis (PCA), a multivariate statistical procedure closely related to factor analysis, has become a widely accepted means of dealing with these problems. Because the true component structure of the ERP data typically analyzed by PCA is unknown, Wood and McCarthy (Electroenceph. clin. Neurophysiol., 1984, 59: 249) used simulated ERP components to investigate the ability of PCA, Varimax rotation, and univariate A N O V A s to reconstruct component wave shapes, to allocate variance correctly across components, and to identify the correct locus of experimental effects. Under the near-optimal conditions employed, PCA reconstructed the wave shapes of the simulated components reasonably well; however, variance was incorrectly al'located across overlapping components, producing dramatic increases in Type l error for ANOVAs on one component when the true treatment effect was on another. Here we extend these results to simulated components with different scalp distributions; such differences are thought to facilitate accurate component extraction by PCA. Large increases in Type 1 error were again obtained, indicating that differences in scalp distribution do not eliminate variance misallocation by PCA.
DPP2.12 T E M P O R A l , R E L A T I O N S H I P OF S U B J E C T I V E P E R C E P T I O N AND T H E N E U R O N A L EVENTS IND U C E D BY P E R I P H E R A L S T I M U L A T I O N . W. Massing
(Langenhagen, W. Germany) Libet et al. stimulated the cortex of h u m a n subjects during the course of surgical treatment and found that perception of the