# coherencypb

## PURPOSE

Multi-taper coherency,cross-spectrum and individual spectra - binned point process

## SYNOPSIS

function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypb(data1,data2,params,fscorr)

## DESCRIPTION

     Multi-taper coherency,cross-spectrum and individual spectra - binned point process

     Usage:

     [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypb(data1,data2,params,fscorr)
     Input:
           data1 (in form samples x trials) -- required
           data2 (in form samples x trials) -- 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

                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
           fscorr   (finite size corrections, 0 (don't use finite size corrections) or
                     1 (use finite size corrections) - optional
                     (available only for spikes). Defaults 0.
     Output:
           C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           S12 (cross spectrum -  frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
           f (frequencies)
           zerosp (1 for trials in either channel where spikes were absent, zero otherwise)
           confC (confidence level for C at 1-p %) - only for err(1)>=1
           phistd - jackknife/theoretical 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:

- check_consistency Helper routine to check consistency of data dimensions
- coherr Function to compute lower and upper confidence intervals on the coherency
- 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
- mtfftpb Multi-taper fourier transform - binned point process data

This function is called by:

- coherencysegpb Multi-taper coherency,cross-spectrum and individual spectra computed by segmenting
- cohgrampb Multi-taper time-frequency coherence,cross-spectrum and individual spectra - two binned point processes
- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypb(data1,data2,params,fscorr)
    0002 % Multi-taper coherency,cross-spectrum and individual spectra - binned point process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencypb(data1,data2,params,fscorr)
    0007 % Input:
    0008 %       data1 (in form samples x trials) -- required
    0009 %       data2 (in form samples x trials) -- required
    0010 %       params: structure with fields tapers, pad, Fs, fpass, err, trialave
    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 %           trialave (average over trials when 1, don't average when 0) - optional. Default 0
    0043 %       fscorr   (finite size corrections, 0 (don't use finite size corrections) or
    0044 %                 1 (use finite size corrections) - optional
    0045 %                 (available only for spikes). Defaults 0.
    0046 % Output:
    0047 %       C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0048 %       phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0049 %       S12 (cross spectrum -  frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0050 %       S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0051 %       S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
    0052 %       f (frequencies)
    0053 %       zerosp (1 for trials in either channel where spikes were absent, zero otherwise)
    0054 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
    0055 %       phistd - jackknife/theoretical standard deviation for phi.  Note that
    0056 %                phi + 2 phistd and phi -2 phistd will give 95% confidence bands
    0057 %                for phi - only for err(1)>=1
    0058 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
    0059 if nargin < 2; error('Need data1 and data2'); end;
    0060 if nargin < 2; error('Need data1 and data2'); end;
    0061 if nargin < 3; params=[]; end;
    0062 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0063 clear params
    0064 if nargin < 4 || isempty(fscorr); fscorr=0; end;
    0065
    0066 if nargout > 9 && err(1)~=2;
    0067     error('Cerr computed only for Jackknife. Correct inputs or outputs and run again');
    0068 end;
    0069 if nargout > 7 && err(1)==0;
    0070     error('When errors are desired, err(1) has to be non-zero.');
    0071 end;
    0072
    0073 [N,Ch]=check_consistency(data1,data2);
    0074 nfft=max(2^(nextpow2(N)+pad),N);
    0075 [f,findx]=getfgrid(Fs,nfft,fpass);
    0076 tapers=dpsschk(tapers,N,Fs); % check tapers
    0077 [J1,Msp,Nsp1]=mtfftpb(data1,tapers,nfft);
    0078 [J2,Msp,Nsp2]=mtfftpb(data2,tapers,nfft);
    0079 zerosp=zeros(1,Ch); % initialize the zerosp variable
    0080 zerosp(Nsp1==0 | Nsp2==0)=1; % set the zerosp variable
    0081 J1=J1(findx,:,:);
    0082 J2=J2(findx,:,:);
    0083 S12=squeeze(mean(conj(J1).*J2,2));
    0084 S1=squeeze(mean(conj(J1).*J1,2));
    0085 S2=squeeze(mean(conj(J2).*J2,2));
    0086 if trialave; S12=squeeze(mean(S12,2)); S1=squeeze(mean(S1,2)); S2=squeeze(mean(S2,2)); end;
    0087 C12=S12./sqrt(S1.*S2);
    0088 C=abs(C12);
    0089 phi=angle(C12);
    0090 if nargout==10;
    0091     if fscorr==1;
    0092        [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,Nsp1,Nsp2);
    0093     else
    0094        [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave);
    0095     end;
    0096 elseif nargout==9;
    0097     if fscorr==1;
    0098         [confC,phistd]=coherr(C,J1,J2,err,trialave,Nsp1,Nsp2);
    0099     else
    0100         [confC,phistd]=coherr(C,J1,J2,err,trialave);
    0101     end;
    0102 end;
    0103 clear Msp