Multi-taper computation of the power and the fstatistic for a particular frequency - continuous process
Usage:
[P,Fstat,f0]=mtpowerandfstatc(data,params,f0)
Input:
Note units have to be consistent. See chronux.m for more information.
data (in form samples x channels/trials or a single vector) -- 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.
f0 (frequency of calculation)
Output:
P (integrated power within the frequency range of interest (trapezoidal integration))
Fstat (F-statistic)
f0 (frequency)0001 function [P,Fstat,f0]=mtpowerandfstatc(data,params,f0) 0002 % Multi-taper computation of the power and the fstatistic for a particular frequency - continuous process 0003 % 0004 % Usage: 0005 % 0006 % [P,Fstat,f0]=mtpowerandfstatc(data,params,f0) 0007 % Input: 0008 % Note units have to be consistent. See chronux.m for more information. 0009 % data (in form samples x channels/trials or a single vector) -- 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 % f0 (frequency of calculation) 0038 % Output: 0039 % P (integrated power within the frequency range of interest (trapezoidal integration)) 0040 % Fstat (F-statistic) 0041 % f0 (frequency) 0042 0043 if nargin < 1; error('Need data'); end; 0044 if nargin < 2; params=[]; end; 0045 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params); 0046 clear fpass err trialave params 0047 data=change_row_to_column(data); 0048 [N,C]=size(data); 0049 tapers=dpsschk(tapers,N,Fs); % calculate the tapers 0050 [N,K]=size(tapers); 0051 nfft=max(2^(nextpow2(N)+pad),N);% number of points in fft 0052 %[f0,findx]=getfgrid(Fs,nfft,f0);% frequency grid to be returned 0053 0054 tapers=tapers(:,:,ones(1,C)); % add channel indices to tapers 0055 data=data(:,:,ones(1,K)); % add taper indices to data 0056 data=permute(data,[1 3 2]); % reshape data to get dimensions to match those of tapers 0057 data_proj=data.*tapers; % product of data with tapers in the form time x tapers x channels 0058 t=(0:N-1)'/Fs; 0059 fourier=exp(-i*2*pi*f0*t); 0060 fourier=fourier(:,ones(1,K),ones(1,C)); 0061 J=squeeze(sum(fourier.*data_proj))/Fs; 0062 0063 Kodd=1:2:K; 0064 Keven=2:2:K; 0065 tapers=tapers(:,:,ones(1,C)); % add channel indices to the tapers - t x K x C 0066 H0 = squeeze(sum(tapers(:,Kodd,:),1)); % calculate sum of tapers for even prolates - K x C 0067 0068 if C==1; H0=H0'; J=J'; end; 0069 P=squeeze(mean(J.*conj(J),1)); 0070 Jp=J(Kodd,:); % drop the even ffts 0071 H0sq=sum(H0.*H0,1);% sum of squares of H0^2 across taper indices - dimensions C 0072 JpH0=sum(Jp.*H0,1);% sum of the product of Jp and H0 across taper indices - f x C\ 0073 A=squeeze(JpH0./H0sq); % amplitudes for all frequencies and channels 0074 Kp=size(Jp,1); % number of even prolates 0075 Ap=A(ones(1,Kp),:); % add the taper index to C 0076 Jhat=Ap.*H0; % fitted value for the fft 0077 0078 num=(K-1).*(abs(A).^2).*squeeze(H0sq);%numerator for F-statistic 0079 den=squeeze(sum(abs(Jp-Jhat).^2,1)+sum(abs(J(Keven,:)).^2,1));% denominator for F-statistic 0080 Fstat=num./den; % F-statisitic 0081