Before analyzing any encephalogram, first remove the artifacts (manually, cut), and also use the method of independent components. After that, you can proceed to the subsequent statistical processing.

"Particularly, the analysing procedure is like this: reading the raw data, then do low-pass filter for LFP, then analying power spectrum of LFP, etc. High-pass filter for spike, then spike-sorting, then estimating firing rate, then do some statistic analysis"

It depends on your specific questions. Generally, for in vivo electrophysiological data pre-whitening is not necessary unless you are interested in performing a gamma frequency location factor analysis on short data segments in which case pre-whitening of LFP data can help to equalizes the variance across frequency bins and decrease frequency leakage during spectral analysis.

You may want to use a notch filter to remove any 60 cycle noise before analyzing the LFPs for power spectral density in a frequency range that overlaps with this noise. For investigations of firing rate and spike timing in relationship LFPs you will also need to speed filter your data. Speed filtering may also be important if you are investigating oscillations that change with movement such as theta and gamma versus sharp wave ripples. As for firing rate of sorted spike clusters you will need to look at the auto-correlograms to determine which clusters are from pyramidal cells versus which are from interneurons prior to analysis; the histograms for pyramidal cell have shorter means and show a burst of activity from 3 to 10 ms. Also make sure you have no activity in the refractory periods of your sorted spike clusters. You may also want to apply a minimum firing rate cut off for pyramidal cells if you are going to be analyzing the activity of these for place fields because units with very low rates can give you false positives. Finally when you are performing your LFP analysis for power use a multiple taper method which are particularly powerful for performing spectral analysis of short data segments and to use decibels rather than mV2/Hz as this will result in the data being more normally distributed.

Dear Yukhymenko,

Thanks for your reply.

In many kinds of analysis of signals, like using autocorrelation function to calculate the power spectrum, need the signal is stationary.

Furthermore, in the filed of time series analysis, as if every method is built in a precondition of "stationary". So I do not know whether it is suitable to use the analysis directly in neuroscience.

Seemingly we are not talking about the same thing.

Dear Ratner

Thank you very much.

The noise-remove of 50/60hz is necessary, so are the other procedures. I'm not sure what is speed filter, are these the window size and moving step of spectrum(or coherence) changing with time?

I gave that outline of analysis because I would like to know when I need pre-whitening. As I know, the Wiener–Khinchin Theorem allows us calculate the power spectral density of LFP, but it needs that signal is stationary. Some other statistical analysis like Granger Causality, also require it is stationary series.

So I would like to know the conditions of pre-processing in electrophysiological data in detail.

All best,

Jichen

Again it depends on what you are trying to analyze the data for. So far you have not provided me with any information to indicate what you are trying to look at that would require whitening. If you just want to look at raw power in frequency band "x" there should be no reason to do anything with the data other than speed filter it so you know when the animal is moving versus when he is stationary as this will influence the LFP power in theta, gamma and sharp wave ripple frequency bands. Alternative you cold filter the data for activity in specific frequency and then only analyze this frequency filtered data for changes due to disease model, or specific behaviors et cetera.

FYI, the multiple taper when used in combination with a 1024-point Fast Fourier Transform should be sufficient to reduce estimation bias due to leakage of energy across spectral frequencies.

If you are still concerned, I suggest using Welch's periodogram for the PSD which avoids the problems associated with classic periodograms which require the spectral content of the signal to be stationnary (i.e. time-unvarying) over the time period. The Welch's method works by averaging the periodograms obtained over short segments of the windows to reduce this variance.

Marcia H. Ratner

For exploiting the data that we recorded, we'll try our best to analyse all kinds of ways.

We recorded in free moving animal with behavioral paradigm, the bahaviors have several conditions. Here are all the analyses that we'll do:

The analyses contain LFP and spike. For LFP, these are whether PSD(in average of a period, or in a moving version) of the frequency of 0.1 to 100hz( containing delta, gamma, etc ) are different in diverse behavioral conditions, and whether LFP of different brain areas' coherence change in different behaviors.

For spike, after spike-sorting, we are going to analyse the firing rate in behaviors( PSTH), and the phase-locking between the LFP and spike. Spikes are more important than LFP in our research.

Moreover, we want to know the directionality of brain areas, so we would use the granger causality test( built in an autoregression model).

The raw data sampling in 30khz, LFP data will down sample to 1khz. As you said, a enough sample points will reduce the estimation bias of PSD. If the segments that we analyse are longer than 1s, which would be more than 1000-point. And if the segments are 0.5s and I use zero-padding to 1024-point, will these are unbias approximately? And how about the spike trains?

The periodogram is also a alternative method to use.

Many thanks.

Yes 1024 should be fine for what you are doing

spike timing analysis will require speed filtering to assess for theta modulation and phase procession as animal moves in and out of place fields in relation to its running speed

Thank you very much, Dr. Ratner

Could you give us more information about the "speed filtering" ?

I do not know what is that. Are there any tutorials or papers to learn?

If the animal is moving in an environment you need to know it’s velocity as this influences theta frequency which increases with speed. If the animal is tracked with LEDs you can use his location versus time to calculated his speed.

So you mean I should try to find the connection between the moving speed and the theta frequency, and to see whether animals' moving affect the frequency of theta?

If it really influences the theta frequency, what would be the next step?

Thank you.

Spike timing changes in relationship to theta as the animal moves into and out of a place field so you can then calculate where the spike occurs in relation to the theta oscillations

Oh, the phase-locking between spikes and theta LFP change with the moving speed. I get it, thank you!