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)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;