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)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