NHP-pRF/Toolboxes/chronux/spectral_analysis/continuous/ftestc.m

function [Fval,A,f,sig,sd] = ftestc(data,params,p,plt)
% 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)
if nargin < 1; error('Need data'); end;
if nargin < 2 || isempty(params); params=[]; end;
[tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
clear err trialave
data=change_row_to_column(data);
[N,C]=size(data);
if nargin<3 || isempty(p);p=0.05/N;end;
if nargin<4 || isempty(plt); plt='n';end;
tapers=dpsschk(tapers,N,Fs); % calculate the tapers
[N,K]=size(tapers);
nfft=max(2^(nextpow2(N)+pad),N);% number of points in fft
[f,findx]=getfgrid(Fs,nfft,fpass);% frequency grid to be returned
% errorchk = 0; % set error checking to default (no errors calculated)
% if nargout <= 3 % if called with 4 output arguments, activate error checking
%     errorchk = 0;
% else
%     errorchk = 1; 
% end 
Kodd=1:2:K;
Keven=2:2:K;
J=mtfftc(data,tapers,nfft,Fs);% tapered fft of data - f x K x C
Jp=J(findx,Kodd,:); % drop the even ffts and restrict fft to specified frequency grid - f x K x C
tapers=tapers(:,:,ones(1,C)); % add channel indices to the tapers - t x K x C
H0 = squeeze(sum(tapers(:,Kodd,:),1)); % calculate sum of tapers for even prolates - K x C 
if C==1;H0=H0';end;
Nf=length(findx);% number of frequencies
H0 = H0(:,:,ones(1,Nf)); % add frequency indices to H0 - K x C x f
H0=permute(H0,[3 1 2]); % permute H0 to get dimensions to match those of Jp - f x K x C 
H0sq=sum(H0.*H0,2);% sum of squares of H0^2 across taper indices - f x C
JpH0=sum(Jp.*squeeze(H0),2);% sum of the product of Jp and H0 across taper indices - f x C
A=squeeze(JpH0./H0sq); % amplitudes for all frequencies and channels
Kp=size(Jp,2); % number of even prolates
Ap=A(:,:,ones(1,Kp)); % add the taper index to C
Ap=permute(Ap,[1 3 2]); % permute indices to match those of H0
Jhat=Ap.*H0; % fitted value for the fft

num=(K-1).*(abs(A).^2).*squeeze(H0sq);%numerator for F-statistic
den=squeeze(sum(abs(Jp-Jhat).^2,2)+sum(abs(J(findx,Keven,:)).^2,2));% denominator for F-statistic
Fval=num./den; % F-statisitic
if nargout > 3
   sig=finv(1-p,2,2*K-2); % F-distribution based 1-p% point
   var=den./(K*squeeze(H0sq)); % variance of amplitude
   sd=sqrt(var);% standard deviation of amplitude
end;
if nargout==0 || strcmp(plt,'y');
   [S,f]=mtspectrumc(detrend(data),params);subplot(211); plot(f,10*log10(S));xlabel('frequency Hz'); ylabel('Spectrum dB');
   subplot(212);plot(f,Fval); line(get(gca,'xlim'),[sig sig],'Color','r');xlabel('frequency Hz');
   ylabel('F ratio');
end
A=A*Fs;