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Spectral analysis II: Applications. Bijan Pesaran Center for Neural Science New York University. Outline. Example I: LFP spectrograms Example II: Spike rates, spectra and coherence Example III: Spike-LFP coherence Example IV: Decoding and single trial analysis
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Spectral analysis II: Applications Bijan Pesaran Center for Neural Science New York University
Outline • Example I: LFP spectrograms • Example II: Spike rates, spectra and coherence • Example III: Spike-LFP coherence • Example IV: Decoding and single trial analysis • Example V: Combining SVD and spectra
Spiking and LFP activity • Extracellular potential Spikes LFP • Current summation determines the amplitude of LFP • Spatial and temporal
How do we analyze spike trains and field potentials together? • Use spectral methods for a hybrid point-continuous process Continuous process LFP Voltage Point process Spike times
Spectrum power Spike times 1/T + power = T Coherency frequency High Low Spikes Field Spectral intuition = LFP Voltage
Example I: LFP spectrograms • LFP recording from Macaque area LIP Cue Memory Saccade Memory Saccade Task Pesaran et al (2002)
Cue Saccade Cue Saccade Example I: LFP spectrograms • Example recording
Example I: LFP spectrograms • Estimation issues • Bias • Narrow band • Broad band • Variance
Example I: LFP spectrograms • Confidence intervals • Chi2 • Assume Gaussian process • Jackknife • Does not assume Gaussian process
Multitaper estimate - Single Trial, [5,9] Periodogram – Single Trial Example I: LFP spectrograms
Example I: LFP spectrograms Periodogram – Single Trial Multitaper estimate - Single Trial
Multitaper estimate - Nine Trials [5,9] Example I: LFP spectrograms Multitaper estimate - Single Trial [5,9]
Example I: LFP spectrograms Multitaper estimate - Single Trial Multitaper estimate - Nine Trials
Multitaper estimate - 95% Jackknife Leave-one-out Example I: LFP spectrograms Multitaper estimate - 95% Chi2
Multitaper estimate - T = 0.2s, W = 25Hz Example I: LFP spectrograms Multitaper estimate - T = 0.5s, W = 10Hz
Example II: Spike rates, spectra and coherence • Simultaneous two-cell recording from Macaque area LIP Cue Delay Reach and Saccade Reach and Saccade Task Pesaran et al (Unpublished)
Locfit estimate nn = 0.1 Example II: Spike rates, spectra and coherence Binning estimate T = 50ms
Example II: Spike rates, spectra and coherence Multitaper spectrum [8,15] Auto-correlation fn
Example II: Spike rates, spectra and coherence • Inter-spike intervals
Example II: Spike rates, spectra and coherence • Inter-spike intervals • Spike spectrum properties • High frequency limit • Low freq suppression • Spectral peaks
Example II: Spike rates, spectra and coherence Multitaper coherence 9 trials, [8,15] Cross-correlation fn
Example II: Spike rates, spectra and coherence Multitaper coherence 9 trials, [8,15] Multitaper coherence 9 trials, [12,23]
Example III: Spike-field coherence • Experimental paradigm Womelsdorf et al (2006)
Example III: Spike-field coherence • Hypothesis testing Womelsdorf et al (2006)
Example III: Spike-field coherence • Single trial analysis Womelsdorf et al (2006)
Example IV: Decoding and single trial analysis • Decoding LFP spectra Pesaran et al (2002)
Example V: SVD and spectra • SVD • Time-channel decomposition • Reduced dimensionality data set • Estimate spectra of modes
Example V: SVD and spectra Fall et al (Unpublished)
Summary • Presented examples of neuronal time series • Compared methods for their analysis • Demonstrated advantages of spectral analysis