computes the F-statistic for sine wave in locally-white noise (continuous data).
[Fval,A,f,sig,sd] = ftestc(data,params,p,plt)
Inputs:
data (data in [N,C] i.e. time x channels/trials or a single
vector) - required.
params structure containing parameters - params has the
following fields: tapers, Fs, fpass, pad
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
Fs (sampling frequency) -- optional. Defaults to 1.
fpass (frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
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.
p (P-value to calculate error bars for) - optional.
Defaults to 0.05/N where N is the number of samples which
corresponds to a false detect probability of approximately 0.05.
plt (y/n for plot and no plot respectively)
Outputs:
Fval (F-statistic in frequency x channels/trials form)
A (Line amplitude for X in frequency x channels/trials form)
f (frequencies of evaluation)
sig (F distribution (1-p)% confidence level)
sd (standard deviation of the amplitude C)0001 function [Fval,A,f,sig,sd] = ftestc(data,params,p,plt) 0002 % computes the F-statistic for sine wave in locally-white noise (continuous data). 0003 % 0004 % [Fval,A,f,sig,sd] = ftestc(data,params,p,plt) 0005 % 0006 % Inputs: 0007 % data (data in [N,C] i.e. time x channels/trials or a single 0008 % vector) - required. 0009 % params structure containing parameters - params has the 0010 % following fields: tapers, Fs, fpass, pad 0011 % tapers : precalculated tapers from dpss or in the one of the following 0012 % forms: 0013 % (1) A numeric vector [TW K] where TW is the 0014 % time-bandwidth product and K is the number of 0015 % tapers to be used (less than or equal to 0016 % 2TW-1). 0017 % (2) A numeric vector [W T p] where W is the 0018 % bandwidth, T is the duration of the data and p 0019 % is an integer such that 2TW-p tapers are used. In 0020 % this form there is no default i.e. to specify 0021 % the bandwidth, you have to specify T and p as 0022 % well. Note that the units of W and T have to be 0023 % consistent: if W is in Hz, T must be in seconds 0024 % and vice versa. Note that these units must also 0025 % be consistent with the units of params.Fs: W can 0026 % be in Hz if and only if params.Fs is in Hz. 0027 % The default is to use form 1 with TW=3 and K=5 0028 % 0029 % Fs (sampling frequency) -- optional. Defaults to 1. 0030 % fpass (frequency band to be used in the calculation in the form 0031 % [fmin fmax])- optional. 0032 % Default all frequencies between 0 and Fs/2 0033 % pad (padding factor for the FFT) - optional (can take values -1,0,1,2...). 0034 % -1 corresponds to no padding, 0 corresponds to padding 0035 % to the next highest power of 2 etc. 0036 % e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT 0037 % to 512 points, if pad=1, we pad to 1024 points etc. 0038 % Defaults to 0. 0039 % p (P-value to calculate error bars for) - optional. 0040 % Defaults to 0.05/N where N is the number of samples which 0041 % corresponds to a false detect probability of approximately 0.05. 0042 % plt (y/n for plot and no plot respectively) 0043 % 0044 % Outputs: 0045 % Fval (F-statistic in frequency x channels/trials form) 0046 % A (Line amplitude for X in frequency x channels/trials form) 0047 % f (frequencies of evaluation) 0048 % sig (F distribution (1-p)% confidence level) 0049 % sd (standard deviation of the amplitude C) 0050 if nargin < 1; error('Need data'); end; 0051 if nargin < 2 || isempty(params); params=[]; end; 0052 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params); 0053 clear err trialave 0054 data=change_row_to_column(data); 0055 [N,C]=size(data); 0056 if nargin<3 || isempty(p);p=0.05/N;end; 0057 if nargin<4 || isempty(plt); plt='n';end; 0058 tapers=dpsschk(tapers,N,Fs); % calculate the tapers 0059 [N,K]=size(tapers); 0060 nfft=max(2^(nextpow2(N)+pad),N);% number of points in fft 0061 [f,findx]=getfgrid(Fs,nfft,fpass);% frequency grid to be returned 0062 % errorchk = 0; % set error checking to default (no errors calculated) 0063 % if nargout <= 3 % if called with 4 output arguments, activate error checking 0064 % errorchk = 0; 0065 % else 0066 % errorchk = 1; 0067 % end 0068 Kodd=1:2:K; 0069 Keven=2:2:K; 0070 J=mtfftc(data,tapers,nfft,Fs);% tapered fft of data - f x K x C 0071 Jp=J(findx,Kodd,:); % drop the even ffts and restrict fft to specified frequency grid - f x K x C 0072 tapers=tapers(:,:,ones(1,C)); % add channel indices to the tapers - t x K x C 0073 H0 = squeeze(sum(tapers(:,Kodd,:),1)); % calculate sum of tapers for even prolates - K x C 0074 if C==1;H0=H0';end; 0075 Nf=length(findx);% number of frequencies 0076 H0 = H0(:,:,ones(1,Nf)); % add frequency indices to H0 - K x C x f 0077 H0=permute(H0,[3 1 2]); % permute H0 to get dimensions to match those of Jp - f x K x C 0078 H0sq=sum(H0.*H0,2);% sum of squares of H0^2 across taper indices - f x C 0079 JpH0=sum(Jp.*squeeze(H0),2);% sum of the product of Jp and H0 across taper indices - f x C 0080 A=squeeze(JpH0./H0sq); % amplitudes for all frequencies and channels 0081 Kp=size(Jp,2); % number of even prolates 0082 Ap=A(:,:,ones(1,Kp)); % add the taper index to C 0083 Ap=permute(Ap,[1 3 2]); % permute indices to match those of H0 0084 Jhat=Ap.*H0; % fitted value for the fft 0085 0086 num=(K-1).*(abs(A).^2).*squeeze(H0sq);%numerator for F-statistic 0087 den=squeeze(sum(abs(Jp-Jhat).^2,2)+sum(abs(J(findx,Keven,:)).^2,2));% denominator for F-statistic 0088 Fval=num./den; % F-statisitic 0089 if nargout > 3 0090 sig=finv(1-p,2,2*K-2); % F-distribution based 1-p% point 0091 var=den./(K*squeeze(H0sq)); % variance of amplitude 0092 sd=sqrt(var);% standard deviation of amplitude 0093 end; 0094 if nargout==0 || strcmp(plt,'y'); 0095 [S,f]=mtspectrumc(detrend(data),params);subplot(211); plot(f,10*log10(S));xlabel('frequency Hz'); ylabel('Spectrum dB'); 0096 subplot(212);plot(f,Fval); line(get(gca,'xlim'),[sig sig],'Color','r');xlabel('frequency Hz'); 0097 ylabel('F ratio'); 0098 end 0099 A=A*Fs;