Home > chronux > spectral_analysis > continuous > mtpowerandfstatc.m

# mtpowerandfstatc

## PURPOSE Multi-taper computation of the power and the fstatistic for a particular frequency - continuous process

## SYNOPSIS function [P,Fstat,f0]=mtpowerandfstatc(data,params,f0)

## DESCRIPTION ``` Multi-taper computation of the power and the fstatistic for a particular frequency - continuous process

Usage:

[P,Fstat,f0]=mtpowerandfstatc(data,params,f0)
Input:
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...).
to the next highest power of 2 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)```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:

## SOURCE CODE ```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...).
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;
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```

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