# coherencysegc

## PURPOSE

Multi-taper coherency, cross-spectrum and individual spectra with segmenting - continuous process

## SYNOPSIS

function [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencysegc(data1,data2,win,params)

## DESCRIPTION

     Multi-taper coherency, cross-spectrum and individual spectra with segmenting - continuous process
       computed by segmenting two univariate time series into chunks

     Usage:
     [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencysegc(data1,data2,win,params)
     Input:
     Note units have to be consistent. See chronux.m for more information.
           data1 (column vector) -- required
           data2 (column vector) -- required
           win   (length of segments) - 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 - frequencies x segments if segave=0; dimension frequencies if segave=1)
           phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
           S12 (cross spectrum -  frequencies x segments if segave=0; dimension frequencies if segave=1)
           S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
           S2 (spectrum 2 - frequencies x segments if segave=0; dimension frequencies if segave=1)
           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
- createdatamatc Helper function to create an event triggered matrix from univariate
- check_consistency Helper routine to check consistency of data dimensions
- 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,f,confC,phistd,Cerr]=coherencysegc(data1,data2,win,params)
    0002 % Multi-taper coherency, cross-spectrum and individual spectra with segmenting - continuous process
    0003 %   computed by segmenting two univariate time series into chunks
    0004 %
    0005 % Usage:
    0006 % [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencysegc(data1,data2,win,params)
    0007 % Input:
    0008 % Note units have to be consistent. See chronux.m for more information.
    0009 %       data1 (column vector) -- required
    0010 %       data2 (column vector) -- required
    0011 %       win   (length of segments) - required
    0012 %       params: structure with fields tapers, pad, Fs, fpass, err
    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 (can take values -1,0,1,2...).
    0033 %                    -1 corresponds to no padding, 0 corresponds to padding
    0034 %                    to the next highest power of 2 etc.
    0035 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0036 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0037 %                       Defaults to 0.
    0038 %           Fs   (sampling frequency) - optional. Default 1.
    0039 %           fpass    (frequency band to be used in the calculation in the form
    0040 %                                   [fmin fmax])- optional.
    0041 %                                   Default all frequencies between 0 and Fs/2
    0042 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0043 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0044 % Output:
    0045 %       C (magnitude of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
    0046 %       phi (phase of coherency - frequencies x segments if segave=0; dimension frequencies if segave=1)
    0047 %       S12 (cross spectrum -  frequencies x segments if segave=0; dimension frequencies if segave=1)
    0048 %       S1 (spectrum 1 - frequencies x segments if segave=0; dimension frequencies if segave=1)
    0049 %       S2 (spectrum 2 - frequencies x segments if segave=0; dimension frequencies if segave=1)
    0050 %       f (frequencies)
    0051 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
    0052 %       phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
    0053 %                Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
    0054 %                bands for phi - only for err(1)>=1
    0055 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
    0056
    0057 if nargin < 3; error('Need data1 and data2 and size of segment'); end;
    0058 if nargin < 4; params=[]; end;
    0059 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0060 clear tapers pad fpass trialave
    0061 if nargout > 8 && err(1)~=2;
    0062     error('Cerr computed only for Jackknife. Correct inputs and run again');
    0063 end;
    0064 if nargout > 6 && err(1)==0;
    0065 %   Errors computed only if err(1) is nonzero. Need to change params and run again.
    0066     error('When errors are desired, err(1) has to be non-zero.');
    0067 end;
    0068 if size(data1,2)~=1 || size(data2,2)~=1; error('works for only univariate time series'); end;
    0069
    0070 N=check_consistency(data1,data2);
    0071
    0072 dt=1/Fs; % sampling interval
    0073 T=N*dt; % length of data in seconds
    0074 E=0:win:T-win; % fictitious event triggers
    0075 win=[0 win]; % use window length to define left and right limits of windows around triggers
    0076 data1=createdatamatc(data1,E,Fs,win); % segmented data 1
    0077 data2=createdatamatc(data2,E,Fs,win); % segmented data 2
    0078 params.trialave=1;
    0079 params.trialave=1;
    0080 if err==0;
    0081    [C,phi,S12,S1,S2,f]=coherencyc(data1,data2,params); % compute coherency for segmented data
    0082 elseif err(1)==1;
    0083    [C,phi,S12,S1,S2,f,confC,phistd]=coherencyc(data1,data2,params); % compute coherency for segmented data
    0084 elseif err(1)==2;
    0085    [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencyc(data1,data2,params); % compute coherency for segmented data
    0086 end;