Multi-taper segmented, second spectrum (spectrum of the log spectrum) for a continuous process
This routine computes the second spectrum by explicitly evaluating the
Fourier transform (since the spectrum is symmetric in frequency, it uses
a cosine transform)
Usage:
[SS,tau]=mtspectrum_of_spectrumc(data,win,tapers2spec,params)
Input:
Note units have to be consistent. See chronux.m for more information.
data (single channel) -- required
win (duration of the segments) - required.
tapers2spec (tapers used for the spectrum of spectrum computation) -
required in the form [use TW K] - Note that spectrum of the
spectrum involves computing two Fourier transforms. While the first
transform (of the original data) is always computed using the
multi-taper method, the current routine allows the user to specify
whether or not to use this method for the second transform. use=1
means use tapers, use=anything other than 1 means do not use the
multitaper method. If use=1, then tapers2spec controls the
smoothing for the second Fourier transform. Otherwise, a direct
Fourier transform is computed.
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
Output:
SS (second spectrum in form frequency x segments x trials x channels
if segave=0; in the form frequency x trials x channels if segave=1)
tau (frequencies)0001 function [SS,tau]=mtspectrum_of_spectrumc(data,win,tapers2spec,params) 0002 % Multi-taper segmented, second spectrum (spectrum of the log spectrum) for a continuous process 0003 % This routine computes the second spectrum by explicitly evaluating the 0004 % Fourier transform (since the spectrum is symmetric in frequency, it uses 0005 % a cosine transform) 0006 % 0007 % Usage: 0008 % 0009 % [SS,tau]=mtspectrum_of_spectrumc(data,win,tapers2spec,params) 0010 % Input: 0011 % Note units have to be consistent. See chronux.m for more information. 0012 % data (single channel) -- required 0013 % win (duration of the segments) - required. 0014 % tapers2spec (tapers used for the spectrum of spectrum computation) - 0015 % required in the form [use TW K] - Note that spectrum of the 0016 % spectrum involves computing two Fourier transforms. While the first 0017 % transform (of the original data) is always computed using the 0018 % multi-taper method, the current routine allows the user to specify 0019 % whether or not to use this method for the second transform. use=1 0020 % means use tapers, use=anything other than 1 means do not use the 0021 % multitaper method. If use=1, then tapers2spec controls the 0022 % smoothing for the second Fourier transform. Otherwise, a direct 0023 % Fourier transform is computed. 0024 % params: structure with fields tapers, pad, Fs, fpass, err, trialave 0025 % - optional 0026 % tapers : precalculated tapers from dpss or in the one of the following 0027 % forms: 0028 % (1) A numeric vector [TW K] where TW is the 0029 % time-bandwidth product and K is the number of 0030 % tapers to be used (less than or equal to 0031 % 2TW-1). 0032 % (2) A numeric vector [W T p] where W is the 0033 % bandwidth, T is the duration of the data and p 0034 % is an integer such that 2TW-p tapers are used. In 0035 % this form there is no default i.e. to specify 0036 % the bandwidth, you have to specify T and p as 0037 % well. Note that the units of W and T have to be 0038 % consistent: if W is in Hz, T must be in seconds 0039 % and vice versa. Note that these units must also 0040 % be consistent with the units of params.Fs: W can 0041 % be in Hz if and only if params.Fs is in Hz. 0042 % The default is to use form 1 with TW=3 and K=5 0043 % 0044 % pad (padding factor for the FFT) - optional (can take values -1,0,1,2...). 0045 % -1 corresponds to no padding, 0 corresponds to padding 0046 % to the next highest power of 2 etc. 0047 % e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT 0048 % to 512 points, if pad=1, we pad to 1024 points etc. 0049 % Defaults to 0. 0050 % Fs (sampling frequency) - optional. Default 1. 0051 % fpass (frequency band to be used in the calculation in the form 0052 % [fmin fmax])- optional. 0053 % Default all frequencies between 0 and 0054 % Fs/2 0055 % Output: 0056 % SS (second spectrum in form frequency x segments x trials x channels 0057 % if segave=0; in the form frequency x trials x channels if segave=1) 0058 % tau (frequencies) 0059 if nargin < 3; error('Need data,segment duration and taper information'); end; 0060 if nargin < 4 ; params=[]; end; 0061 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params); 0062 [N,Ntr,NC]=size(data); 0063 if Ntr==1; error('cannot compute second spectrum with just one trial'); end; 0064 dt=1/Fs; % sampling interval 0065 T=N*dt; % length of data in seconds 0066 E=0:win:T-win; % fictitious event triggers 0067 datatmp=createdatamatc(data(:,1,1),E,Fs,[0 win]); % segmented data 0068 Ninseg=size(datatmp,1); % number of samples in segments 0069 nfft=max(2^(nextpow2(Ninseg)+pad),Ninseg); 0070 [f,findx]=getfgrid(Fs,nfft,fpass); 0071 NF=length(findx); 0072 S=zeros(NF,Ntr,NC); 0073 for nc=1:NC; 0074 for ntr=1:Ntr; 0075 datatmp=change_row_to_column(data(:,ntr,nc)); 0076 s=mtspectrumsegc(datatmp,win,params,1); 0077 S(:,ntr,nc)=s; 0078 end 0079 end; 0080 Sm=mean(S,2); 0081 if use==1; 0082 params.tapers=tapers2spec; 0083 params.Fs=1/(f(2)-f(1)); 0084 params.fpass=[0 params.Fs/2]; 0085 else; 0086 tau=[0:NF-1]/max(f); 0087 cosinefunc=cos(2*pi*f'*tau); 0088 end; 0089 0090 for nc=1:NC; 0091 for ntr=1:Ntr; 0092 s=S(:,ntr,nc)./Sm(:,nc); 0093 s=log(s); 0094 if use==1; 0095 sflip=flipdim(s,1); 0096 s=[sflip(1:NF-1);s]; 0097 [ss,tau]=mtspectrumc(s,params); 0098 SS(:,ntr,nc)=ss; 0099 else; 0100 s=repmat(s,[1 NF]).*cosinefunc; 0101 % subplot(221); plot(s(:,1)); 0102 % subplot(222); plot(s(:,10)); 0103 % subplot(223); plot(s(:,100)); 0104 % subplot(224); plot(s(:,120)); 0105 % pause 0106 s=trapz(f,s,1)'; 0107 ss=s.*conj(s); 0108 % plot(tau,s) 0109 % pause 0110 end 0111 SS(:,ntr,nc)=ss; 0112 end 0113 end; 0114 SS=mean(SS,2);