CrossSpecMat

 Multi-taper cross-spectral matrix - another routine, this one allows for multiple trials and channels 
 but does not do confidence intervals. Also this routine always averages over trials - continuous process

 Usage:

 [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMat(data,win,params)
 Input: 
 Note units have to be consistent. See chronux.m for more information.
       data (in form samples x channels x trials) 
       win  (duration of non-overlapping window)
       params: structure with fields tapers, pad, Fs, fpass
       - 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. Defaults to 0.  
                       e.g. For N = 500, if PAD = 0, we pad the FFT 
                       to 512 points; if PAD = 2, we pad the FFT
                       to 2048 points, etc.
           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
 Output:
       Sc (cross spectral matrix frequency x channels x channels)
       Cmat Coherence matrix frequency x channels x channels
       Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
       Cvec leading Eigenvector (frequency x channels)
       Cent A different measure of total coherence: GM/AM of SV^2s
       f (frequencies)

0001 function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMat(data,win,params)
0002 %
0003 %
0004 % Multi-taper cross-spectral matrix - another routine, this one allows for multiple trials and channels
0005 % but does not do confidence intervals. Also this routine always averages over trials - continuous process
0006 %
0007 % Usage:
0008 %
0009 % [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMat(data,win,params)
0010 % Input:
0011 % Note units have to be consistent. See chronux.m for more information.
0012 %       data (in form samples x channels x trials)
0013 %       win  (duration of non-overlapping window)
0014 %       params: structure with fields tapers, pad, Fs, fpass
0015 %       - optional
0016 %           tapers (precalculated tapers from dpss, or in the form [NW K] e.g [3 5]) -- optional.
0017 %                                                 If not specified, use [NW K]=[3 5]
0018 %            pad            (padding factor for the FFT) - optional. Defaults to 0.
0019 %                       e.g. For N = 500, if PAD = 0, we pad the FFT
0020 %                       to 512 points; if PAD = 2, we pad the FFT
0021 %                       to 2048 points, etc.
0022 %           Fs   (sampling frequency) - optional. Default 1.
0023 %           fpass    (frequency band to be used in the calculation in the form
0024 %                                   [fmin fmax])- optional.
0025 %                                   Default all frequencies between 0 and Fs/2
0026 % Output:
0027 %       Sc (cross spectral matrix frequency x channels x channels)
0028 %       Cmat Coherence matrix frequency x channels x channels
0029 %       Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
0030 %       Cvec leading Eigenvector (frequency x channels)
0031 %       Cent A different measure of total coherence: GM/AM of SV^2s
0032 %       f (frequencies)
0033 d=ndims(data);
0034 if d<2, error('Need multidimensional array'); end
0035 if d==2, [N,C]=size(data); end;
0036 if d==3, [N,C,Ntr]=size(data); end; 
0037 if nargin < 3; params=[]; end;
0038 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
0039 clear err trialave params
0040 nwin=round(win*Fs); nfft=2^(nextpow2(nwin)+pad); 
0041 [f,findx]=getfgrid(Fs,nfft,fpass); 
0042 tapers=dpsschk(tapers,nwin,Fs); % check tapers
0043 Sc=zeros(length(findx),C,C);
0044 
0045 Nwins=floor(N/nwin);
0046 
0047 if d==3, % If there are multiple trials
0048 for iwin=1:Nwins,
0049     for i=1:Ntr, 
0050         data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:,i));
0051         J1=mtfftc(detrend(data1),tapers,nfft,Fs);
0052         J1=J1(findx,:,:);
0053         for k=1:C,
0054             for l=1:C,
0055                 spec=squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2)); 
0056             Sc(:,k,l)=Sc(:,k,l)+spec;
0057             end
0058         end
0059     end
0060 end
0061 Sc=Sc/(Nwins*Ntr);
0062 end
0063 
0064 if d==2, % only one trial
0065 for iwin=1:Nwins,
0066         data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:));
0067         J1=mtfftc(data1,tapers,nfft,Fs);
0068         J1=J1(findx,:,:);
0069         for k=1:C,
0070             for l=1:C,
0071             Sc(:,k,l)=Sc(:,k,l)+squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2));
0072             end
0073         end
0074 end
0075 Sc=Sc/Nwins;
0076 end
0077 
0078 Cmat=Sc;
0079 Sdiag=zeros(length(findx),C);
0080 for k=1:C,
0081     Sdiag(:,k)=squeeze(Sc(:,k,k));
0082 end
0083 
0084 for k=1:C,
0085     for l=1:C,
0086         Cmat(:,k,l)=Sc(:,k,l)./sqrt(abs(Sdiag(:,k).*Sdiag(:,l)));
0087     end
0088 end
0089 
0090 Ctot=zeros(length(findx),1); Cent=Ctot;
0091 Cvec=zeros(length(findx),C);
0092 for i=1:length(findx),
0093     [u s]=svd(squeeze(Sc(i,:,:)));s=diag(s);
0094     Ctot(i)=s(1).^2/sum(s.^2); Cent(i)=exp(mean(log(s.^2)))/mean(s.^2);             
0095     Cvec(i,:)=transpose(u(:,1));
0096 
0097 end
0098