Multi-taper segmented spectrum for a univariate continuous process
Usage:
[S,f,varS,C,Serr]=mtspectrumsegc(data,win,params,segave)
Input:
Note units have to be consistent. See chronux.m for more information.
data (single channel) -- required
win (duration of the segments) - 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.
fpass (frequency band to be used in the calculation in the form
[fmin fmax])- optional.
Default all frequencies between 0 and Fs/2
err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
[0 p] or 0 - no error bars) - optional. Default 0.
trialave - not used
segave - optional 0 for don't average over segments, 1 for average - default
1
Output:
S (spectrum in form frequency x segments if segave=0; in the form frequency if segave=1)
f (frequencies)
varS (variance of the log spectrum)
C (covariance matrix of the log spectrum - frequency x
frequency matrix)
Serr (error bars) only for err(1)>=10001 function [S,f,varS,C,Serr]=mtspectrumsegc(data,win,params,segave) 0002 % Multi-taper segmented spectrum for a univariate continuous process 0003 % 0004 % Usage: 0005 % 0006 % [S,f,varS,C,Serr]=mtspectrumsegc(data,win,params,segave) 0007 % Input: 0008 % Note units have to be consistent. See chronux.m for more information. 0009 % data (single channel) -- required 0010 % win (duration of the segments) - required. 0011 % params: structure with fields tapers, pad, Fs, fpass, err, trialave 0012 % - optional 0013 % tapers : precalculated tapers from dpss or in the one of the following 0014 % forms: 0015 % (1) A numeric vector [TW K] where TW is the 0016 % time-bandwidth product and K is the number of 0017 % tapers to be used (less than or equal to 0018 % 2TW-1). 0019 % (2) A numeric vector [W T p] where W is the 0020 % bandwidth, T is the duration of the data and p 0021 % is an integer such that 2TW-p tapers are used. In 0022 % this form there is no default i.e. to specify 0023 % the bandwidth, you have to specify T and p as 0024 % well. Note that the units of W and T have to be 0025 % consistent: if W is in Hz, T must be in seconds 0026 % and vice versa. Note that these units must also 0027 % be consistent with the units of params.Fs: W can 0028 % be in Hz if and only if params.Fs is in Hz. 0029 % The default is to use form 1 with TW=3 and K=5 0030 % 0031 % pad (padding factor for the FFT) - optional (can take values -1,0,1,2...). 0032 % -1 corresponds to no padding, 0 corresponds to padding 0033 % to the next highest power of 2 etc. 0034 % e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT 0035 % to 512 points, if pad=1, we pad to 1024 points etc. 0036 % Defaults to 0. 0037 % Fs (sampling frequency) - optional. Default 1. 0038 % fpass (frequency band to be used in the calculation in the form 0039 % [fmin fmax])- optional. 0040 % Default all frequencies between 0 and Fs/2 0041 % err (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars 0042 % [0 p] or 0 - no error bars) - optional. Default 0. 0043 % trialave - not used 0044 % segave - optional 0 for don't average over segments, 1 for average - default 0045 % 1 0046 % Output: 0047 % S (spectrum in form frequency x segments if segave=0; in the form frequency if segave=1) 0048 % f (frequencies) 0049 % varS (variance of the log spectrum) 0050 % C (covariance matrix of the log spectrum - frequency x 0051 % frequency matrix) 0052 % Serr (error bars) only for err(1)>=1 0053 0054 if nargin < 2; error('Need data and segment information'); end; 0055 data=change_row_to_column(data); 0056 if size(data,2)~=1; error('works for only univariate time series'); end; 0057 if nargin < 3 ; params=[]; end; 0058 if nargin < 4 || isempty(segave); segave=1; end; 0059 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params); clear trialave params 0060 if nargout==4 && err(1)==0; 0061 % Errors can't be computed if err(1)=0. Need to change params and run again. 0062 error('When Serr is desired, err(1) has to be non-zero.'); 0063 end; 0064 N=size(data,1); % length of segmented data 0065 dt=1/Fs; % sampling interval 0066 T=N*dt; % length of data in seconds 0067 E=0:win:T-win; % fictitious event triggers 0068 win=[0 win]; % use window length to define left and right limits of windows around triggers 0069 data=createdatamatc(data,E,Fs,win); % segmented data 0070 N=size(data,1); % length of segmented data 0071 nfft=max(2^(nextpow2(N)+pad),N); 0072 [f,findx]=getfgrid(Fs,nfft,fpass); 0073 tapers=dpsschk(tapers,N,Fs); % check tapers 0074 J=mtfftc(data,tapers,nfft,Fs); % compute tapered fourier transforms 0075 J=J(findx,:,:); % restrict to specified frequencies 0076 S=squeeze(mean(conj(J).*J,2)); % spectra of non-overlapping segments (average over tapers) 0077 if segave==1; SS=squeeze(mean(S,2)); else; SS=S;end; % mean of the spectrum averaged across segments 0078 if nargout > 2 0079 lS=log(S); % log spectrum for nonoverlapping segments 0080 varS=var(lS',1)'; % variance of log spectrum 0081 % varS=var(lS',1)';% variance of the log spectrum R13 0082 if nargout > 3 0083 C=cov(lS'); % covariance matrix of the log spectrum 0084 if nargout==5; 0085 Serr=specerr(SS,J,err,segave); 0086 end; 0087 end; 0088 end; 0089 S=SS;