


Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times
Usage:
[C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t)
Input:
data1 (continuous data in time x trials form) -- required
data2 (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- required
params: structure with fields tapers, pad, Fs, fpass, err, trialave
- optional
tapers (precalculated tapers from dpss, or in the form [NW K] e.g [3 5]) -- optional. If not
specified, use [NW K]=[3 5]
pad (padding factor for the FFT) - optional (can take values -1,0,1,2...).
-1 corresponds to no padding, 0 corresponds to padding
to the next highest power of 2 etc.
e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
to 512 points, if pad=1, we pad to 1024 points etc.
Defaults to 0.
Fs (sampling frequency) - optional. Default 1.
fpass (frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave (average over trials when 1, don't average when 0) - optional. Default 0
fscorr (finite size corrections, 0 (don't use finite size corrections) or 1 (use finite size corrections) - optional
(available only for spikes). Defaults 0.
t (time grid over which the tapers are to be calculated:
this argument is useful when calling the spectrum
calculation routine from a moving window spectrogram
calculation routine). If left empty, the spike times
are used to define the grid.
Output:
C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
f (frequencies)
zerosp (1 for trials where no spikes were found, 0 otherwise)
confC (confidence level for C at 1-p %) - only for err(1)>=1
phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi - Note that
phi + 2 phistd and phi - 2 phistd will give 95% confidence
bands for phi - only for err(1)>=1
Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2)

0001 function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t) 0002 % Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times 0003 % 0004 % Usage: 0005 % 0006 % [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t) 0007 % Input: 0008 % data1 (continuous data in time x trials form) -- required 0009 % data2 (structure array of spike times with dimension trials; also accepts 1d array of spike times) -- required 0010 % params: structure with fields tapers, pad, Fs, fpass, err, trialave 0011 % - optional 0012 % tapers (precalculated tapers from dpss, or in the form [NW K] e.g [3 5]) -- optional. If not 0013 % specified, use [NW K]=[3 5] 0014 % pad (padding factor for the FFT) - optional (can take values -1,0,1,2...). 0015 % -1 corresponds to no padding, 0 corresponds to padding 0016 % to the next highest power of 2 etc. 0017 % e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT 0018 % to 512 points, if pad=1, we pad to 1024 points etc. 0019 % Defaults to 0. 0020 % Fs (sampling frequency) - optional. Default 1. 0021 % fpass (frequency band to be used in the calculation in the form 0022 % [fmin fmax])- optional. 0023 % Default all frequencies between 0 and Fs/2 0024 % err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars 0025 % [0 p] or 0 - no error bars) - optional. Default 0. 0026 % trialave (average over trials when 1, don't average when 0) - optional. Default 0 0027 % fscorr (finite size corrections, 0 (don't use finite size corrections) or 1 (use finite size corrections) - optional 0028 % (available only for spikes). Defaults 0. 0029 % t (time grid over which the tapers are to be calculated: 0030 % this argument is useful when calling the spectrum 0031 % calculation routine from a moving window spectrogram 0032 % calculation routine). If left empty, the spike times 0033 % are used to define the grid. 0034 % Output: 0035 % C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0036 % phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0037 % S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0038 % S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0039 % S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0040 % f (frequencies) 0041 % zerosp (1 for trials where no spikes were found, 0 otherwise) 0042 % confC (confidence level for C at 1-p %) - only for err(1)>=1 0043 % phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi - Note that 0044 % phi + 2 phistd and phi - 2 phistd will give 95% confidence 0045 % bands for phi - only for err(1)>=1 0046 % Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2) 0047 if nargin < 2; error('Need data1 and data2'); end; 0048 if nargin < 3; params=[]; end; 0049 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params); 0050 clear params 0051 if nargin < 4 || isempty(fscorr); fscorr=0; end; 0052 if nargin < 5 || isempty(t); 0053 [N,C]=size(data1); 0054 dt=1/Fs; 0055 t=0:dt:(N-1)*dt; % time grid for prolates 0056 end; 0057 if nargout > 7 && err(1)==0; 0058 % Errors computed only if err(1) is non-zero. Need to change params and run again. 0059 error('When errors are desired, err(1) has to be non-zero.'); 0060 end; 0061 if nargout > 9 && err(1)~=2; 0062 error('Cerr computed only for Jackknife. Correct inputs and run again'); 0063 end; 0064 0065 [N,Ch]=check_consistency(data1,data2,1); 0066 zerosp=zeros(1,Ch); % intialize the zerosp variable 0067 N=length(t); % number of points in grid for dpss 0068 nfft=max(2^(nextpow2(N)+pad),N); % number of points in fft of prolates 0069 [f,findx]=getfgrid(Fs,nfft,fpass); 0070 tapers=dpsschk(tapers,N,Fs); % check tapers 0071 J1=mtfftc(data1,tapers,nfft,Fs); % fourier transform of continuous data 0072 J1=J1(findx,:,:); % restrict to required frequencies 0073 [J2,Msp2,Nsp2]=mtfftpt(data2,tapers,nfft,t,f,findx); % fourier transform of discrete data 0074 zerosp(Nsp2==0)=1; % set zerosp to 1 for trials where no spikes were found 0075 S12=squeeze(mean(conj(J1).*J2,2)); % cross spectrum 0076 S1=squeeze(mean(conj(J1).*J1,2)); % spectrum data 1 0077 S2=squeeze(mean(conj(J2).*J2,2)); % spectrum data 2 0078 if trialave; S12=squeeze(mean(S12,2)); S1=squeeze(mean(S1,2)); S2=squeeze(mean(S2,2)); end; 0079 C12=S12./sqrt(S1.*S2); 0080 C=abs(C12); 0081 phi=angle(C12); 0082 if nargout==10; 0083 if fscorr==1; 0084 [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,[],Nsp2); 0085 else 0086 [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave); 0087 end; 0088 elseif nargout==9; 0089 if fscorr==1; 0090 [confC,phistd]=coherr(C,J1,J2,err,trialave,[],Nsp2); 0091 else 0092 [confC,phistd]=coherr(C,J1,J2,err,trialave); 0093 end; 0094 end; 0095 clear Msp2