# cohgramc

## PURPOSE

Multi-taper time-frequency coherence,cross-spectrum and individual spectra - continuous processes

## SYNOPSIS

function [C,phi,S12,S1,S2,t,f,confC,phistd,Cerr]=cohgramc(data1,data2,movingwin,params)

## DESCRIPTION

     Multi-taper time-frequency coherence,cross-spectrum and individual spectra - continuous processes

     Usage:

     [C,phi,S12,S1,S2,t,f,confC,phistd,Cerr]=cohgramc(data1,data2,movingwin,params)
     Input:
     Note units have to be consistent. Thus, if movingwin is in seconds, Fs
     has to be in Hz. see chronux.m for more information.

           data1 (in form samples x trials) -- required
           data2 (in form samples x trials) -- required
           movingwin (in the form [window winstep] -- required
           params: structure with fields tapers, pad, Fs, fpass, err, trialave
           - 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
                         Note that T has to be equal to movingwin(1).

                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
     Output:
           C (magnitude of coherency time x frequencies x trials for trialave=0;
                 time x frequency for trialave=1)
           phi (phase of coherency time x frequencies x trials for no trial averaging;
                 time x frequency for trialave=1)
           S12 (cross spectrum - time x frequencies x trials for no trial averaging;
                 time x frequency for trialave=1)
           S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
                 time x frequency for trialave=1)
           S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
                 time x frequency for trialave=1)
           t (time)
           f (frequencies)
           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)

## CROSS-REFERENCE INFORMATION

This function calls:

- coherencyc Multi-taper coherency,cross-spectrum and individual spectra - continuous process
- check_consistency Helper routine to check consistency of data dimensions
- 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:

- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [C,phi,S12,S1,S2,t,f,confC,phistd,Cerr]=cohgramc(data1,data2,movingwin,params)
    0002 % Multi-taper time-frequency coherence,cross-spectrum and individual spectra - continuous processes
    0003 %
    0004 % Usage:
    0005 %
    0006 % [C,phi,S12,S1,S2,t,f,confC,phistd,Cerr]=cohgramc(data1,data2,movingwin,params)
    0007 % Input:
    0008 % Note units have to be consistent. Thus, if movingwin is in seconds, Fs
    0009 % has to be in Hz. see chronux.m for more information.
    0010 %
    0011 %       data1 (in form samples x trials) -- required
    0012 %       data2 (in form samples x trials) -- required
    0013 %       movingwin (in the form [window winstep] -- required
    0014 %       params: structure with fields tapers, pad, Fs, fpass, err, trialave
    0015 %       - optional
    0016 %           tapers : precalculated tapers from dpss or in the one of the following
    0017 %                    forms:
    0018 %                    (1) A numeric vector [TW K] where TW is the
    0019 %                        time-bandwidth product and K is the number of
    0020 %                        tapers to be used (less than or equal to
    0021 %                        2TW-1).
    0022 %                    (2) A numeric vector [W T p] where W is the
    0023 %                        bandwidth, T is the duration of the data and p
    0024 %                        is an integer such that 2TW-p tapers are used. In
    0025 %                        this form there is no default i.e. to specify
    0026 %                        the bandwidth, you have to specify T and p as
    0027 %                        well. Note that the units of W and T have to be
    0028 %                        consistent: if W is in Hz, T must be in seconds
    0029 %                        and vice versa. Note that these units must also
    0030 %                        be consistent with the units of params.Fs: W can
    0031 %                        be in Hz if and only if params.Fs is in Hz.
    0032 %                        The default is to use form 1 with TW=3 and K=5
    0033 %                     Note that T has to be equal to movingwin(1).
    0034 %
    0035 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0036 %                    -1 corresponds to no padding, 0 corresponds to padding
    0037 %                    to the next highest power of 2 etc.
    0038 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0039 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0040 %                       Defaults to 0.
    0041 %           Fs   (sampling frequency) - optional. Default 1.
    0042 %           fpass    (frequency band to be used in the calculation in the form
    0043 %                                   [fmin fmax])- optional.
    0044 %                                   Default all frequencies between 0 and Fs/2
    0045 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0046 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0047 %           trialave (average over trials when 1, don't average when 0) - optional. Default 0
    0048 % Output:
    0049 %       C (magnitude of coherency time x frequencies x trials for trialave=0;
    0050 %             time x frequency for trialave=1)
    0051 %       phi (phase of coherency time x frequencies x trials for no trial averaging;
    0052 %             time x frequency for trialave=1)
    0053 %       S12 (cross spectrum - time x frequencies x trials for no trial averaging;
    0054 %             time x frequency for trialave=1)
    0055 %       S1 (spectrum 1 - time x frequencies x trials for no trial averaging;
    0056 %             time x frequency for trialave=1)
    0057 %       S2 (spectrum 2 - time x frequencies x trials for no trial averaging;
    0058 %             time x frequency for trialave=1)
    0059 %       t (time)
    0060 %       f (frequencies)
    0061 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
    0062 %       phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
    0063 %                Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
    0064 %                bands for phi - only for err(1)>=1
    0065 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
    0066
    0067 if nargin < 3; error('Need data1 and data2 and window parameters'); end;
    0068 if nargin < 4; params=[];end;
    0069
    0070 if length(params.tapers)==3 & movingwin(1)~=params.tapers(2);
    0071     error('Duration of data in params.tapers is inconsistent with movingwin(1), modify params.tapers(2) to proceed')
    0072 end
    0073
    0074 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0075
    0076 if nargout > 9 && err(1)~=2;
    0077     error('Cerr computed only for Jackknife. Correct inputs and run again');
    0078 end;
    0079 if nargout > 7 && err(1)==0;
    0080 %   Errors computed only if err(1) is nonzero. Need to change params and run again.
    0081     error('When errors are desired, err(1) has to be non-zero.');
    0082 end;
    0083 [N,Ch]=check_consistency(data1,data2);
    0084
    0085 Nwin=round(Fs*movingwin(1)); % number of samples in window
    0086 Nstep=round(movingwin(2)*Fs); % number of samples to step through
    0087 nfft=max(2^(nextpow2(Nwin)+pad),Nwin);
    0088 f=getfgrid(Fs,nfft,fpass);
    0089 Nf=length(f);
    0090 params.tapers=dpsschk(tapers,Nwin,Fs); % check tapers
    0091
    0092 winstart=1:Nstep:N-Nwin+1;
    0093 nw=length(winstart);
    0094 if trialave;
    0095    C=zeros(nw,Nf);
    0096    S12=zeros(nw,Nf);
    0097    S1=zeros(nw,Nf);
    0098    S2=zeros(nw,Nf);
    0099    phi=zeros(nw,Nf);
    0100    Cerr=zeros(2,nw,Nf);
    0101 %    phierr=zeros(2,nw,Nf);
    0102    phistd=zeros(nw,Nf);
    0103 else
    0104    C=zeros(nw,Nf,Ch);
    0105    S12=zeros(nw,Nf,Ch);
    0106    S1=zeros(nw,Nf,Ch);
    0107    S2=zeros(nw,Nf,Ch);
    0108    phi=zeros(nw,Nf,Ch);
    0109    Cerr=zeros(2,nw,Nf,Ch);
    0110 %    phierr=zeros(2,nw,Nf,Ch);
    0111    phistd=zeros(nw,Nf,Ch);
    0112 end;
    0113
    0114 for n=1:nw;
    0115    indx=winstart(n):winstart(n)+Nwin-1;
    0116    datawin1=data1(indx,:);datawin2=data2(indx,:);
    0117    if nargout==10;
    0118      [c,ph,s12,s1,s2,f,confc,phie,cerr]=coherencyc(datawin1,datawin2,params);
    0119 %      phierr(1,n,:,:)=squeeze(phie(1,:,:));
    0120 %      phierr(2,n,:,:)=squeeze(phie(2,:,:));
    0121      phistd(n,:,:)=phie;
    0122      Cerr(1,n,:,:)=squeeze(cerr(1,:,:));
    0123      Cerr(2,n,:,:)=squeeze(cerr(2,:,:));
    0124    elseif nargout==9;
    0125      [c,ph,s12,s1,s2,f,confc,phie]=coherencyc(datawin1,datawin2,params);
    0126 %      phierr(1,n,:,:)=squeeze(phie(1,:,:));
    0127 %      phierr(2,n,:,:)=squeeze(phie(2,:,:));
    0128       phistd(n,:,:)=phie;
    0129    else
    0130      [c,ph,s12,s1,s2,f]=coherencyc(datawin1,datawin2,params);
    0131    end;
    0132    C(n,:,:)=c;
    0133    S12(n,:,:)=s12;
    0134    S1(n,:,:)=s1;
    0135    S2(n,:,:)=s2;
    0136    phi(n,:,:)=ph;
    0137 end;
    0138 C=squeeze(C); phi=squeeze(phi);S12=squeeze(S12); S1=squeeze(S1); S2=squeeze(S2);
    0139 if nargout > 8; confC=confc; end;
    0140 if nargout==10;Cerr=squeeze(Cerr);end;
    0141 % if nargout>=9; phierr=squeeze(phierr);end
    0142 if nargout>=9; phistd=squeeze(phistd);end
    0143 winmid=winstart+round(Nwin/2);
    0144 t=winmid/Fs;