Multi-taper coherency,cross-spectrum and individual spectra - continuous process
Usage:
[C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencyc(data1,data2,params)
Input:
Note units have to be consistent. See chronux.m for more information.
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
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)
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)0001 function [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencyc(data1,data2,params) 0002 % Multi-taper coherency,cross-spectrum and individual spectra - continuous process 0003 % 0004 % Usage: 0005 % [C,phi,S12,S1,S2,f,confC,phistd,Cerr]=coherencyc(data1,data2,params) 0006 % Input: 0007 % Note units have to be consistent. See chronux.m for more information. 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 % Output: 0044 % C (magnitude of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0045 % phi (phase of coherency - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0046 % S12 (cross spectrum - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0047 % S1 (spectrum 1 - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0048 % S2 (spectrum 2 - frequencies x trials if trialave=0; dimension frequencies if trialave=1) 0049 % f (frequencies) 0050 % confC (confidence level for C at 1-p %) - only for err(1)>=1 0051 % phistd - theoretical/jackknife (depending on err(1)=1/err(1)=2) standard deviation for phi. 0052 % Note that phi + 2 phistd and phi - 2 phistd will give 95% confidence 0053 % bands for phi - only for err(1)>=1 0054 % Cerr (Jackknife error bars for C - use only for Jackknife - err(1)=2) 0055 0056 if nargin < 2; error('Need data1 and data2'); end; 0057 data1=change_row_to_column(data1); 0058 data2=change_row_to_column(data2); 0059 if nargin < 3; params=[]; end; 0060 [tapers,pad,Fs,fpass,err,trialave]=getparams(params); 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 N=check_consistency(data1,data2); 0069 nfft=max(2^(nextpow2(N)+pad),N); 0070 [f,findx]=getfgrid(Fs,nfft,fpass); 0071 tapers=dpsschk(tapers,N,Fs); % check tapers 0072 J1=mtfftc(data1,tapers,nfft,Fs); 0073 J2=mtfftc(data2,tapers,nfft,Fs); 0074 J1=J1(findx,:,:); J2=J2(findx,:,:); 0075 S12=squeeze(mean(conj(J1).*J2,2)); 0076 S1=squeeze(mean(conj(J1).*J1,2)); 0077 S2=squeeze(mean(conj(J2).*J2,2)); 0078 if trialave; S12=squeeze(mean(S12,2)); S1=squeeze(mean(S1,2)); S2=squeeze(mean(S2,2)); end; 0079 C12=S12./sqrt(S1.*S2); 0080 C=abs(C12); 0081 phi=angle(C12); 0082 if nargout>=9; 0083 [confC,phistd,Cerr]=coherr(C,J1,J2,err,trialave); 0084 elseif nargout==8; 0085 [confC,phistd]=coherr(C,J1,J2,err,trialave); 0086 end;