# mtspectrumsegpb

## PURPOSE

Multi-taper segmented spectrum for a univariate binned point process

## SYNOPSIS

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

## DESCRIPTION

     Multi-taper segmented spectrum for a univariate binned point process

     Usage:

     [S,f,R,varS,zerosp,C,Serr]=mtspectrumsegpb(data,win,params,segave,fscorr)
     Input:
     Note units have to be consistent. See chronux.m for more information.
           data (single vector) -- 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 (1 for averaging across segments, 0 otherwise; 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; as a function of frequency if segave=1)
           f       (frequencies)
           R       (spike rate)
           varS    (variance of the log spectrum)
           zerosp  (0 for segments in which spikes were found, 1 for segments
           in which there are no spikes)
           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:

- 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
- createdatamatpb
- mtfftpb Multi-taper fourier transform - binned point process data

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]=mtspectrumsegpb(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]=mtspectrumsegpb(data,win,params,segave,fscorr)
    0007 % Input:
    0008 % Note units have to be consistent. See chronux.m for more information.
    0009 %       data (single vector) -- required
    0010 %       win  (duration of the segments) - required.
    0011 %       params: structure with fields tapers, pad, Fs, fpass, err
    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 %       segave (1 for averaging across segments, 0 otherwise; default 1)
    0044 %       fscorr   (finite size corrections, 0 (don't use finite size corrections) or
    0045 %                1 (use finite size corrections) - optional
    0046 %                (available only for spikes). Defaults 0.
    0047 % Output:
    0048 %       S       (spectrum in form frequency x segments if segave=0; as a function of frequency if segave=1)
    0049 %       f       (frequencies)
    0050 %       R       (spike rate)
    0051 %       varS    (variance of the log spectrum)
    0052 %       zerosp  (0 for segments in which spikes were found, 1 for segments
    0053 %       in which there are no spikes)
    0054 %       C       (covariance matrix of the log spectrum - frequency x
    0055 %       frequency matrix)
    0056 %       Serr    (error bars) - only for err(1)>=1
    0057
    0058
    0059 if nargin < 2; error('Need data and segment information'); end;
    0060 if nargin < 3; params=[]; end;
    0061 if nargin < 4 || isempty(segave); segave=1; end;
    0062 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0063 clear params trialave
    0064 if nargin < 3 || isempty(fscorr); fscorr=0;end;
    0065
    0066 if nargout > 4 && err(1)==0;
    0067 %   Cannot compute error bars with err(1)=0. Need to change params and run again.
    0068     error('When Serr is desired, err(1) has to be non-zero.');
    0069 end;
    0070 data=change_row_to_column(data);
    0071 N=size(data,1); % total length of data
    0072 dt=1/Fs; % sampling interval
    0073 T=N*dt; % length of data in seconds
    0074 E=0:win:T-win; % fictitious event triggers
    0075 win=[0 win]; % use window length to define left and right limits of windows around triggers
    0076 data=createdatamatpb(data,E,Fs,win);
    0077 N=size(data,1); % length of segmented data
    0078 nfft=max(2^(nextpow2(N)+pad),N);
    0079 [f,findx]=getfgrid(Fs,nfft,fpass);
    0080 tapers=dpsschk(tapers,N,Fs); % check tapers
    0081 [J,Msp,Nsp]=mtfftpb(data,tapers,nfft);
    0082 J=J(findx,:,:);
    0083 R=Msp*Fs;
    0084 S=squeeze(mean(conj(J).*J,2)); % spectra of non-overlapping segments (averaged over tapers)
    0085 if segave==1; SS=squeeze(mean(S,2));R=mean(R);else;SS=S;end;% mean of the spectrum averaged across segments
    0086 if nargout > 3
    0087     lS=log(SS); % log spectrum for nonoverlapping segments
    0088 %     varS=var(lS,1,2); % variance of log spectrum
    0089     varS=var(lS',1)';% variance of the log spectrum R13
    0090     if nargout > 4
    0091        zerosp=zeros(1,size(data,2));
    0092        zerosp(Nsp==0)=1;
    0093        if nargout > 5
    0094           C=cov(lS'); % covariance matrix of the log spectrum
    0095           if nargout==7;
    0096              if fscorr==1;
    0097                 Serr=specerr(SS,J,err,segave,Nsp);
    0098              else
    0099                 Serr=specerr(SS,J,err,segave);
    0100              end;
    0101           end;
    0102        end;
    0103     end;
    0104 end;
    0105 S=SS;