coherencycpt

PURPOSE ^

Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times

SYNOPSIS ^

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

DESCRIPTION ^

 Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times

 Usage:

 [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t)
 Input: 
       data1        (continuous data in time x trials form) -- required
       data2        (structure array of spike times with dimension trials; 
                     also accepts 1d array of spike times) -- 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.
       t        (time grid over which the tapers are to be calculated:
                      this argument is useful when calling the spectrum
                      calculation routine from a moving window spectrogram
                      calculation routine). If left empty, the spike times
                      are used to define the grid.
 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 where no spikes were found, 0 otherwise)
       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: This function is called by:

SOURCE CODE ^

0001 function [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t)
0002 % Multi-taper coherency,cross-spectrum and individual spectra -continuous data and point process as times
0003 %
0004 % Usage:
0005 %
0006 % [C,phi,S12,S1,S2,f,zerosp,confC,phistd,Cerr]=coherencycpt(data1,data2,params,fscorr,t)
0007 % Input:
0008 %       data1        (continuous data in time x trials form) -- required
0009 %       data2        (structure array of spike times with dimension trials;
0010 %                     also accepts 1d array of spike times) -- required
0011 %       params: structure with fields tapers, pad, Fs, fpass, err, trialave
0012 %       - optional
0013 %           tapers : precalculated tapers from dpss or in the one of the following
0014 %                    forms:
0015 %                   (1) A numeric vector [TW K] where TW is the
0016 %                       time-bandwidth product and K is the number of
0017 %                       tapers to be used (less than or equal to
0018 %                       2TW-1).
0019 %                   (2) A numeric vector [W T p] where W is the
0020 %                       bandwidth, T is the duration of the data and p
0021 %                       is an integer such that 2TW-p tapers are used. In
0022 %                       this form there is no default i.e. to specify
0023 %                       the bandwidth, you have to specify T and p as
0024 %                       well. Note that the units of W and T have to be
0025 %                       consistent: if W is in Hz, T must be in seconds
0026 %                       and vice versa. Note that these units must also
0027 %                       be consistent with the units of params.Fs: W can
0028 %                       be in Hz if and only if params.Fs is in Hz.
0029 %                       The default is to use form 1 with TW=3 and K=5
0030 %
0031 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
0032 %                    -1 corresponds to no padding, 0 corresponds to padding
0033 %                    to the next highest power of 2 etc.
0034 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
0035 %                       to 512 points, if pad=1, we pad to 1024 points etc.
0036 %                       Defaults to 0.
0037 %           Fs   (sampling frequency) - optional. Default 1.
0038 %           fpass    (frequency band to be used in the calculation in the form
0039 %                                   [fmin fmax])- optional.
0040 %                                   Default all frequencies between 0 and Fs/2
0041 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
0042 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
0043 %           trialave (average over trials when 1, don't average when 0) - optional. Default 0
0044 %       fscorr   (finite size corrections, 0 (don't use finite size corrections) or
0045 %                                          1 (use finite size corrections) - optional
0046 %                (available only for spikes). Defaults 0.
0047 %       t        (time grid over which the tapers are to be calculated:
0048 %                      this argument is useful when calling the spectrum
0049 %                      calculation routine from a moving window spectrogram
0050 %                      calculation routine). If left empty, the spike times
0051 %                      are used to define the grid.
0052 % Output:
0053 %       C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
0054 %       phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
0055 %       S12 (cross spectrum -  frequencies x trials if trialave=0; dimension frequencies if trialave=1)
0056 %       S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
0057 %       S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1)
0058 %       f (frequencies)
0059 %       zerosp (1 for trials where no spikes were found, 0 otherwise)
0060 %       confC (confidence level for C at 1-p %) - only for err(1)>=1
0061 %       phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi
0062 %                Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence
0063 %                bands for phi - only for err(1)>=1
0064 %       Cerr  (Jackknife error bars for C - use only for Jackknife - err(1)=2)
0065 if nargin < 2; error('Need data1 and data2'); end;
0066 if nargin < 3; params=[]; end;
0067 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
0068 clear params
0069 if nargin < 4 || isempty(fscorr); fscorr=0; end;
0070 if nargin < 5 || isempty(t); 
0071   [N,C]=size(data1);
0072   dt=1/Fs;
0073   t=0:dt:(N-1)*dt; % time grid for prolates
0074 end;
0075 if nargout > 7 && err(1)==0;
0076 %   Errors computed only if err(1) is non-zero. Need to change params and run again.
0077     error('When errors are desired, err(1) has to be non-zero.');
0078 end;
0079 if nargout > 9 && err(1)~=2; 
0080     error('Cerr computed only for Jackknife. Correct inputs and run again');
0081 end;
0082 
0083 [N,Ch]=check_consistency(data1,data2,1);
0084 zerosp=zeros(1,Ch); % intialize the zerosp variable
0085 N=length(t); % number of points in grid for dpss
0086 nfft=max(2^(nextpow2(N)+pad),N); % number of points in fft of prolates
0087 [f,findx]=getfgrid(Fs,nfft,fpass); 
0088 tapers=dpsschk(tapers,N,Fs); % check tapers
0089 J1=mtfftc(data1,tapers,nfft,Fs); % fourier transform of continuous data
0090 J1=J1(findx,:,:); % restrict to required frequencies
0091 [J2,Msp2,Nsp2]=mtfftpt(data2,tapers,nfft,t,f,findx); % fourier transform of discrete data
0092 zerosp(Nsp2==0)=1; % set zerosp to 1 for trials where no spikes were found
0093 S12=squeeze(mean(conj(J1).*J2,2)); % cross spectrum
0094 S1=squeeze(mean(conj(J1).*J1,2)); % spectrum data 1
0095 S2=squeeze(mean(conj(J2).*J2,2)); % spectrum data 2
0096 if trialave; S12=squeeze(mean(S12,2)); S1=squeeze(mean(S1,2)); S2=squeeze(mean(S2,2)); end;
0097 C12=S12./sqrt(S1.*S2);
0098 C=abs(C12);
0099 phi=angle(C12);
0100 if nargout==10; 
0101   if fscorr==1; 
0102      [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave,[],Nsp2); 
0103   else
0104      [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave); 
0105   end;
0106 elseif nargout==9;
0107   if fscorr==1; 
0108      [confC,phistd]=coherr(C,J1,J2,err,trialave,[],Nsp2); 
0109   else
0110      [confC,phistd]=coherr(C,J1,J2,err,trialave); 
0111   end;
0112 end;
0113 clear Msp2

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