# mtspectrumsegpt

## PURPOSE

Multi-taper segmented spectrum for a univariate binned point process

## SYNOPSIS

function [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpt(data,win,params,segave,fscorr)

## DESCRIPTION

     Multi-taper segmented spectrum for a univariate binned point process

     Usage:

     [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpt(data,win,params,segave,fscorr)
     Input:
     Note units have to be consistent. See chronux.m for more information.
           data (structure array of one channel of spike times;
                also accepts 1d vector of spike times) -- required
           win  (duration of the segments) - required.
           params: structure with fields tapers, pad, Fs, fpass, err
           - 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.
           segave - (0 for don't average over segments, 1 for average) - optional - default  1
           fscorr   (finite size corrections, 0 (don't use finite size corrections) or
                    1 (use finite size corrections) - optional
                    (available only for spikes). Defaults 0.
     Output:
           S       (spectrum in form frequency x segments if segave=0; function of frequency if segave=1)
           f       (frequencies)
           R       (spike rate)
           varS    (variance of the spectrum as a function of frequency)
           zerosp  (0 for segments in which spikes were found, 1 for segments
           C       (covariance matrix of the log spectrum - frequency x
           frequency matrix)
           Serr    (error bars) - only if err(1)>=1

## CROSS-REFERENCE INFORMATION

This function calls:

- 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
- createdatamatpt Helper function to create an event triggered matrix from a single
- minmaxsptimes Find the minimum and maximum of the spike times in each channel
- mtfftpt Multi-taper fourier transform for point process given as times

This function is called by:

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

## SOURCE CODE

    0001 function [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpt(data,win,params,segave,fscorr)
    0002 % Multi-taper segmented spectrum for a univariate binned point process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpt(data,win,params,segave,fscorr)
    0007 % Input:
    0008 % Note units have to be consistent. See chronux.m for more information.
    0009 %       data (structure array of one channel of spike times;
    0010 %            also accepts 1d vector of spike times) -- required
    0011 %       win  (duration of the segments) - required.
    0012 %       params: structure with fields tapers, pad, Fs, fpass, err
    0013 %       - optional
    0014 %           tapers : precalculated tapers from dpss or in the one of the following
    0015 %                    forms:
    0016 %                   (1) A numeric vector [TW K] where TW is the
    0017 %                       time-bandwidth product and K is the number of
    0018 %                       tapers to be used (less than or equal to
    0019 %                       2TW-1).
    0020 %                   (2) A numeric vector [W T p] where W is the
    0021 %                       bandwidth, T is the duration of the data and p
    0022 %                       is an integer such that 2TW-p tapers are used. In
    0023 %                       this form there is no default i.e. to specify
    0024 %                       the bandwidth, you have to specify T and p as
    0025 %                       well. Note that the units of W and T have to be
    0026 %                       consistent: if W is in Hz, T must be in seconds
    0027 %                       and vice versa. Note that these units must also
    0028 %                       be consistent with the units of params.Fs: W can
    0029 %                       be in Hz if and only if params.Fs is in Hz.
    0030 %                       The default is to use form 1 with TW=3 and K=5
    0031 %
    0032 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0033 %                    -1 corresponds to no padding, 0 corresponds to padding
    0034 %                    to the next highest power of 2 etc.
    0035 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0036 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0037 %                       Defaults to 0.
    0038 %           Fs   (sampling frequency) - optional. Default 1.
    0039 %           fpass    (frequency band to be used in the calculation in the form
    0040 %                                   [fmin fmax])- optional.
    0041 %                                   Default all frequencies between 0 and Fs/2
    0042 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0043 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0044 %       segave - (0 for don't average over segments, 1 for average) - optional - default  1
    0045 %       fscorr   (finite size corrections, 0 (don't use finite size corrections) or
    0046 %                1 (use finite size corrections) - optional
    0047 %                (available only for spikes). Defaults 0.
    0048 % Output:
    0049 %       S       (spectrum in form frequency x segments if segave=0; function of frequency if segave=1)
    0050 %       f       (frequencies)
    0051 %       R       (spike rate)
    0052 %       varS    (variance of the spectrum as a function of frequency)
    0053 %       zerosp  (0 for segments in which spikes were found, 1 for segments
    0054 %       C       (covariance matrix of the log spectrum - frequency x
    0055 %       frequency matrix)
    0056 %       Serr    (error bars) - only if err(1)>=1
    0057
    0058 if nargin < 2; error('Need data and segment information'); end;
    0059 if nargin < 3; params=[]; end;
    0060 if nargin < 4 || isempty(segave); segave=1; end;
    0061 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0062 clear params trialave
    0063 if nargin < 5 || isempty(fscorr); fscorr=0;end;
    0064
    0065 if nargout > 4 && err(1)==0; error('cannot compute error bars with err(1)=0; change params and run again'); end;
    0066
    0067 dtmp=change_row_to_column(data);
    0068 T=max(dtmp); % total length of data
    0069 minT=min(dtmp);
    0070 E=minT:win:T-win; % fictitious event triggers
    0071 win=[0 win]; % use window length to define left and right limits of windows around triggers
    0072 dtmp=createdatamatpt(dtmp,E,win); % create segmented data set
    0073 [mintime,maxtime]=minmaxsptimes(dtmp);
    0074 dt=1/Fs; % sampling time
    0075 t=mintime-dt:dt:maxtime+dt; % time grid for prolates
    0076 N=length(t); % number of points in grid for dpss
    0077 nfft=max(2^(nextpow2(N)+pad),N); % number of points in fft of prolates
    0078 [f,findx]=getfgrid(Fs,nfft,fpass); % get frequency grid for evaluation
    0079 tapers=dpsschk(tapers,N,Fs); % check tapers
    0080 [J,Msp,Nsp]=mtfftpt(dtmp,tapers,nfft,t,f,findx);% mt fft for point process times
    0081 R=Msp*Fs;
    0082 S=squeeze(mean(conj(J).*J,2)); % spectra of non-overlapping segments (averaged over tapers)
    0083 if segave==1; SS=squeeze(mean(S,2));R=mean(R);else;SS=S;end;% mean of the spectrum averaged across segments
    0084 if nargout > 3
    0085     lS=log(SS); % log spectrum for nonoverlapping segments
    0086 %     varS=var(lS,1,2); % variance of log spectrum
    0087     varS=var(lS',1)';% variance of the log spectrum R13
    0088     if nargout > 4
    0089        zerosp=zeros(1,size(data,2));
    0090        zerosp(Nsp==0)=1;
    0091        if nargout > 5
    0092           C=cov(lS'); % covariance matrix of the log spectrum
    0093           if nargout==7;
    0094              if fscorr==1;
    0095                 Serr=specerr(SS,J,err,segave,Nsp);
    0096              else
    0097                 Serr=specerr(SS,J,err,segave);
    0098              end;
    0099           end;
    0100        end;
    0101     end;
    0102 end;
    0103 S=SS;