# 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
- change_row_to_column Helper routine to transform 1d arrays into column vectors that are needed
- dpsschk Helper function to calculate tapers and, if precalculated tapers are supplied,
- getfgrid Helper function that gets the frequency grid associated with a given fft based computation
- getparams Helper function to convert structure params to variables used by the
- specerr Function to compute lower and upper confidence intervals on the spectrum

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.
- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## 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
    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;