Home > chronux > spectral_analysis > continuous > mtspectrumsegc.m

# mtspectrumsegc

## PURPOSE Multi-taper segmented spectrum for a univariate continuous process

## SYNOPSIS function [S,f,varS,C,Serr]=mtspectrumsegc(data,win,params,segave)

## DESCRIPTION ``` 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)>=1```

## CROSS-REFERENCE INFORMATION This function calls:
• createdatamatc Helper function to create an event triggered matrix from univariate
• mtfftc Multi-taper fourier transform - continuous data
This function is called by:
• mtspectrum_of_spectrumc Multi-taper segmented, second spectrum (spectrum of the log spectrum) for a continuous process
• rmlinesmovingwinc fits significant sine waves to data (continuous data) using overlapping windows.

## SOURCE CODE ```0001 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
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;```

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