# CrossSpecMatc

## PURPOSE

Multi-taper cross-spectral matrix - another routine, allows for multiple trials and channels

## SYNOPSIS

function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)

## DESCRIPTION

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

     Usage:

     [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(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 one of the following
                        forms:
                       (1) A numeric vector [TW K] where TW is the
                           time-bandwidth product and K is the number of
                           tapers to be used (less than or equal to
                           2TW-1).
                       (2) A numeric vector [W T p] where W is the
                           bandwidth, T is the duration of the data and p
                           is an integer such that 2TW-p tapers are used. In
                           this form there is no default i.e. to specify
                           the bandwidth, you have to specify T and p as
                           well. Note that the units of W and T have to be
                           consistent: if W is in Hz, T must be in seconds
                           and vice versa. Note that these units must also
                           be consistent with the units of params.Fs: W can
                           be in Hz if and only if params.Fs is in Hz.
                           The default is to use form 1 with TW=3 and K=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)

## CROSS-REFERENCE INFORMATION

This function calls:

- mtfftc Multi-taper fourier transform - continuous data
- dpsschk Helper function to calculate tapers and, if precalculated tapers are supplied,
- getfgrid Helper function that gets the frequency grid associated with a given fft based computation
- getparams Helper function to convert structure params to variables used by the

This function is called by:

## SOURCE CODE

    0001 function [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)
    0002 % Multi-taper cross-spectral matrix - another routine, allows for multiple trials and channels
    0003 % Does not do confidence intervals. Also this routine always averages over trials - continuous process
    0004 %
    0005 % Usage:
    0006 %
    0007 % [Sc,Cmat,Ctot,Cvec,Cent,f]=CrossSpecMatc(data,win,params)
    0008 % Input:
    0009 % Note units have to be consistent. See chronux.m for more information.
    0010 %       data (in form samples x channels x trials)
    0011 %       win  (duration of non-overlapping window)
    0012 %       params: structure with fields tapers, pad, Fs, fpass
    0013 %       - optional
    0014 %           tapers : precalculated tapers from dpss or in the one of the following
    0015 %                    forms:
    0016 %                   (1) A numeric vector [TW K] where TW is the
    0017 %                       time-bandwidth product and K is the number of
    0018 %                       tapers to be used (less than or equal to
    0019 %                       2TW-1).
    0020 %                   (2) A numeric vector [W T p] where W is the
    0021 %                       bandwidth, T is the duration of the data and p
    0022 %                       is an integer such that 2TW-p tapers are used. In
    0023 %                       this form there is no default i.e. to specify
    0024 %                       the bandwidth, you have to specify T and p as
    0025 %                       well. Note that the units of W and T have to be
    0026 %                       consistent: if W is in Hz, T must be in seconds
    0027 %                       and vice versa. Note that these units must also
    0028 %                       be consistent with the units of params.Fs: W can
    0029 %                       be in Hz if and only if params.Fs is in Hz.
    0030 %                       The default is to use form 1 with TW=3 and K=5
    0031 %
    0032 %            pad            (padding factor for the FFT) - optional. Defaults to 0.
    0033 %                       e.g. For N = 500, if PAD = 0, we pad the FFT
    0034 %                       to 512 points; if PAD = 2, we pad the FFT
    0035 %                       to 2048 points, etc.
    0036 %           Fs   (sampling frequency) - optional. Default 1.
    0037 %           fpass    (frequency band to be used in the calculation in the form
    0038 %                                   [fmin fmax])- optional.
    0039 %                                   Default all frequencies between 0 and Fs/2
    0040 % Output:
    0041 %       Sc (cross spectral matrix frequency x channels x channels)
    0042 %       Cmat Coherence matrix frequency x channels x channels
    0043 %       Ctot Total coherence: SV(1)^2/sum(SV^2) (frequency)
    0044 %       Cvec leading Eigenvector (frequency x channels)
    0045 %       Cent A different measure of total coherence: GM/AM of SV^2s
    0046 %       f (frequencies)
    0047 d=ndims(data);
    0048 if d<2, error('Need multidimensional array'); end
    0049 if d==2, [N,C]=size(data); end;
    0050 if d==3, [N,C,Ntr]=size(data); end;
    0051 if nargin < 3; params=[]; end;
    0052 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0053 clear err trialave params
    0054 nwin=round(win*Fs); nfft=max(2^(nextpow2(nwin)+pad),nwin);
    0055 [f,findx]=getfgrid(Fs,nfft,fpass);
    0056 tapers=dpsschk(tapers,nwin,Fs); % check tapers
    0057 Sc=zeros(length(findx),C,C);
    0058
    0059 Nwins=floor(N/nwin);
    0060
    0061 if d==3, % If there are multiple trials
    0062 for iwin=1:Nwins,
    0063     for i=1:Ntr,
    0064         data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:,i));
    0065         J1=mtfftc(detrend(data1),tapers,nfft,Fs);
    0066         J1=J1(findx,:,:);
    0067         for k=1:C,
    0068             for l=1:C,
    0069                 spec=squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2));
    0070             Sc(:,k,l)=Sc(:,k,l)+spec;
    0071             end
    0072         end
    0073     end
    0074 end
    0075 Sc=Sc/(Nwins*Ntr);
    0076 end
    0077
    0078 if d==2, % only one trial
    0079 for iwin=1:Nwins,
    0080         data1=squeeze(data(1+(iwin-1)*nwin:iwin*nwin,:));
    0081         J1=mtfftc(data1,tapers,nfft,Fs);
    0082         J1=J1(findx,:,:);
    0083         for k=1:C,
    0084             for l=1:C,
    0085             Sc(:,k,l)=Sc(:,k,l)+squeeze(mean(conj(J1(:,:,k)).*J1(:,:,l),2));
    0086             end
    0087         end
    0088 end
    0089 Sc=Sc/Nwins;
    0090 end
    0091
    0092 Cmat=Sc;
    0093 Sdiag=zeros(length(findx),C);
    0094 for k=1:C,
    0095     Sdiag(:,k)=squeeze(Sc(:,k,k));
    0096 end
    0097
    0098 for k=1:C,
    0099     for l=1:C,
    0100         Cmat(:,k,l)=Sc(:,k,l)./sqrt(abs(Sdiag(:,k).*Sdiag(:,l)));
    0101     end
    0102 end
    0103
    0104 Ctot=zeros(length(findx),1); Cent=Ctot;
    0105 Cvec=zeros(length(findx),C);
    0106 for i=1:length(findx),
    0107     [u s]=svd(squeeze(Sc(i,:,:)));s=diag(s);
    0108     Ctot(i)=s(1)/sum(s); Cent(i)=exp(mean(log(s)))/mean(s);
    0109     Cvec(i,:)=transpose(u(:,1));
    0110 end
    0111