Post on 20-Dec-2015
Goals• Practical issues of spectral representation
• Spectral estimation problem
• Examples on real data
Spectral intuition
=tv
LFP Voltage +
Spectrum
pow
er
1/T
ntSpike times
=T
frequency
pow
er
Low High 0
Spikes
Field
Coherency
Fundamental concepts
• Positive and negative frequency
• Nyquist frequency – aliasing
• Rayleigh frequency
• Spectral density and power
ttk coscos
t cos
K even
K odd
dffS2/1
0
2 )(2
Example I: LFP spectrograms
• Estimation issues– Bias
• Narrow band• Broad band
– Variance
– Degrees of freedom
Example I: LFP spectrograms
• Confidence intervals– Chi2
• Assume Gaussian process
– Jackknife• Does not assume Gaussian process
Example I: LFP spectrograms
Multitaper estimate- Single Trial [5,9]
Multitaper estimate- Nine Trials [5,9]
Example I: LFP spectrograms
Multitaper estimate- 95% Chi2
212~ dofS
Multitaper estimate- 95% Jackknife
Leave-one-out
Example I: LFP spectrograms
Time (s)
Fre
quen
cy (
Hz)
-0.5 0 0.5 1 1.50
50
100
5
10
15
20
25
Multitaper estimate- T = 0.5s, W = 10Hz
Time (s)
Fre
quen
cy (
Hz)
-0.5 0 0.5 1 1.50
50
100
150
5
10
15
20
25
Multitaper estimate- T = 0.2s, W = 25Hz
Example II: Spike rates, spectra and coherence
Cross-correlation fn Multitaper coherence9 trials, [8,15]