# cohmatrixc

## PURPOSE

Multi-taper coherency,cross-spectral matrix - continuous process

## SYNOPSIS

function [C,phi,S12,f,confC,phistd,Cerr]=cohmatrixc(data,params)

## DESCRIPTION

     Multi-taper coherency,cross-spectral matrix - continuous process

     Usage:

     [C,phi,S12,f,confC,phistd,Cerr]=cohmatrixc(data,params)
     Input:
     Note units have to be consistent. See chronux.m for more information.
           data (in form samples x channels) -- required
           params: structure with fields tapers, pad, Fs, fpass, err
           - 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 (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.
     Output:
           C (magnitude of coherency frequency x channels x channels)
           phi (phase of coherency frequency x channels x channels)
           S12 (cross-spectral matrix frequency x channels x channels)
           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:

- mtfftc Multi-taper fourier transform - continuous data
- cohmathelper Helper function called by coherency matrix computations.
- 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,f,confC,phistd,Cerr]=cohmatrixc(data,params)
    0002 % Multi-taper coherency,cross-spectral matrix - continuous process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [C,phi,S12,f,confC,phistd,Cerr]=cohmatrixc(data,params)
    0007 % Input:
    0008 % Note units have to be consistent. See chronux.m for more information.
    0009 %       data (in form samples x channels) -- required
    0010 %       params: structure with fields tapers, pad, Fs, fpass, err
    0011 %       - optional
    0012 %           tapers : precalculated tapers from dpss or in the one of the following
    0013 %                    forms:
    0014 %                    (1) A numeric vector [TW K] where TW is the
    0015 %                        time-bandwidth product and K is the number of
    0016 %                        tapers to be used (less than or equal to
    0017 %                        2TW-1).
    0018 %                    (2) A numeric vector [W T p] where W is the
    0019 %                        bandwidth, T is the duration of the data and p
    0020 %                        is an integer such that 2TW-p tapers are used. In
    0021 %                        this form there is no default i.e. to specify
    0022 %                        the bandwidth, you have to specify T and p as
    0023 %                        well. Note that the units of W and T have to be
    0024 %                        consistent: if W is in Hz, T must be in seconds
    0025 %                        and vice versa. Note that these units must also
    0026 %                        be consistent with the units of params.Fs: W can
    0027 %                        be in Hz if and only if params.Fs is in Hz.
    0028 %                        The default is to use form 1 with TW=3 and K=5
    0029 %
    0030 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0031 %                    -1 corresponds to no padding, 0 corresponds to padding
    0032 %                    to the next highest power of 2 etc.
    0033 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0034 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0035 %                       Defaults to 0.
    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 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0041 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0042 % Output:
    0043 %       C (magnitude of coherency frequency x channels x channels)
    0044 %       phi (phase of coherency frequency x channels x channels)
    0045 %       S12 (cross-spectral matrix frequency x channels x channels)
    0046 %       f (frequencies)
    0047 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
    0048 %       phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
    0049 %                Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
    0050 %                bands for phi - only for err(1)>=1
    0051 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
    0052
    0053 if nargin < 1; error('need data'); end;
    0054 if nargin < 2; params=[]; end;
    0055 [N,Ch]=size(data);
    0056 if Ch==1; error('Need at least two channels of data'); end;
    0057 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0058 clear trialave params
    0059 if nargout > 6 && err(1)~=2;
    0060     error('Cerr computed only for Jackknife. Correct inputs and run again');
    0061 end;
    0062 if nargout >= 4 && err(1)==0;
    0063 %   Errors computed only if err(1) is nonzero. Need to change params and run again.
    0064     error('When errors are desired, err(1) has to be non-zero.');
    0065 end;
    0066 nfft=max(2^(nextpow2(N)+pad),N);
    0067 [f,findx]=getfgrid(Fs,nfft,fpass);
    0068 tapers=dpsschk(tapers,N,Fs); % check tapers
    0069 J=mtfftc(data,tapers,nfft,Fs);
    0070 J=J(findx,:,:);
    0071 if err(1)==0;
    0072      [C,phi,S12]=cohmathelper(J,err);
    0073 elseif err(1)==1;
    0074      [C,phi,S12,confC,phistd]=cohmathelper(J,err);
    0075 elseif err(1)==2;
    0076      [C,phi,S12,confC,phistd,Cerr]=cohmathelper(J,err);
    0077 end