# Phase concentration for a broad range of frequency over time

I have local-field potential signals from two animals and I am trying to do phase analysis on these signals. What I am interested in is how phase concentration (or interatrial phase coherence) changes over the course of the signals similar to the figure below (Figure 3A from https://www.jneurosci.org/content/jneuro/31/50/18423.full.pdf): The properties of the signal: Length: 2s Fs: 1000Hz Data structure: [2441 trials, 2001 timepoints]

My approach was to:

1. Filter the signal for all trials in the frequency range of interest (3 - 9 Hz) using a 500th order FIR filter fir1(500,[3 9]/500 );
2. take the Hilbert Transform of the signals (Hilbert function in Matlab)
3. take the instantaneous phase by using "angle" in Matlab
4. Then use "circ_r" in circular statics toolbox (or using the formula: abs(mean(exp(1i * Phase), 1)) ) to calculate the circular R-value.
5. Plot phase over time

This is what I get: The overall trend (peaks of data) is similar to what I expect but there are lots of sharp fluctuations in the phase.

I understand that this might be caused by filter design and leakage from other higher frequencies. I also tried the Maxflat filter or FIR signal with different orders but still get noisy phase response.

I would appreciate if you can help me to solve this issue.