# mtdspectrumpt

## PURPOSE

Multi-taper spectral derivative - point process times

## SYNOPSIS

function [dS,f]=mtdspectrumpt(data,phi,params,t)

## DESCRIPTION

     Multi-taper spectral derivative - point process times

     Usage:

     [dS,f]=mtdspectrumpt(data,phi,params,t)
     Input:
       Note that all times can be in arbitrary units. But the units have to be
       consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
       be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
       times, the units have to be consistent with the units of data as well.
           data        (structure array of spike times with dimension channels/trials;
                       also accepts 1d array of spike times) -- required
           phi         (angle for evaluation of derivative) -- required.
                           e.g. phi=[0,pi/2] giving the time and frequency derivatives
           params: structure with fields tapers, pad, Fs, fpass, 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
               trialave (average over trials when 1, don't average when 0) -
               optional. Default 0
           t        (time grid over which the tapers are to be calculated:
                          this argument is useful when calling the spectrum
                          calculation routine from a moving window spectrogram
                          calculation routine). If left empty, the spike times
                          are used to define the grid.
     Output:
           dS      (spectral derivative in form phi x frequency x channels/trials if trialave=0;
                   function of phi x frequency if trialave=1)
           f       (frequencies)

## 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
- 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:

- mtdspecgrampt Multi-taper derivative time-frequency spectrum - point process times
- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [dS,f]=mtdspectrumpt(data,phi,params,t)
    0002 % Multi-taper spectral derivative - point process times
    0003 %
    0004 % Usage:
    0005 %
    0006 % [dS,f]=mtdspectrumpt(data,phi,params,t)
    0007 % Input:
    0008 %   Note that all times can be in arbitrary units. But the units have to be
    0009 %   consistent. So, if E is in secs, win, t have to be in secs, and Fs has to
    0010 %   be Hz. If E is in samples, so are win and t, and Fs=1. In case of spike
    0011 %   times, the units have to be consistent with the units of data as well.
    0012 %       data        (structure array of spike times with dimension channels/trials;
    0013 %                   also accepts 1d array of spike times) -- required
    0014 %       phi         (angle for evaluation of derivative) -- required.
    0015 %                       e.g. phi=[0,pi/2] giving the time and frequency derivatives
    0016 %       params: structure with fields tapers, pad, Fs, fpass, trialave
    0017 %       -optional
    0018 %           tapers : precalculated tapers from dpss or in the one of the following
    0019 %                    forms:
    0020 %                   (1) A numeric vector [TW K] where TW is the
    0021 %                       time-bandwidth product and K is the number of
    0022 %                       tapers to be used (less than or equal to
    0023 %                       2TW-1).
    0024 %                   (2) A numeric vector [W T p] where W is the
    0025 %                       bandwidth, T is the duration of the data and p
    0026 %                       is an integer such that 2TW-p tapers are used. In
    0027 %                       this form there is no default i.e. to specify
    0028 %                       the bandwidth, you have to specify T and p as
    0029 %                       well. Note that the units of W and T have to be
    0030 %                       consistent: if W is in Hz, T must be in seconds
    0031 %                       and vice versa. Note that these units must also
    0032 %                       be consistent with the units of params.Fs: W can
    0033 %                       be in Hz if and only if params.Fs is in Hz.
    0034 %                       The default is to use form 1 with TW=3 and K=5
    0035 %
    0036 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0037 %                    -1 corresponds to no padding, 0 corresponds to padding
    0038 %                    to the next highest power of 2 etc.
    0039 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0040 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0041 %                       Defaults to 0.
    0042 %           Fs   (sampling frequency) - optional. Default 1.
    0043 %           fpass    (frequency band to be used in the calculation in the form
    0044 %                                   [fmin fmax])- optional.
    0045 %                                   Default all frequencies between 0 and Fs/2
    0046 %           trialave (average over trials when 1, don't average when 0) -
    0047 %           optional. Default 0
    0048 %       t        (time grid over which the tapers are to be calculated:
    0049 %                      this argument is useful when calling the spectrum
    0050 %                      calculation routine from a moving window spectrogram
    0051 %                      calculation routine). If left empty, the spike times
    0052 %                      are used to define the grid.
    0053 % Output:
    0054 %       dS      (spectral derivative in form phi x frequency x channels/trials if trialave=0;
    0055 %               function of phi x frequency if trialave=1)
    0056 %       f       (frequencies)
    0057 if nargin < 2; error('Need data and angle'); end;
    0058 if nargin < 3; params=[]; end;
    0059 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0060 clear err params
    0061 data=change_row_to_column(data);
    0062 dt=1/Fs; % sampling time
    0063 if nargin < 4;
    0064    [mintime,maxtime]=minmaxsptimes(data);
    0065    t=mintime:dt:maxtime+dt; % time grid for prolates
    0066 end;
    0067 N=length(t); % number of points in grid for dpss
    0068 nfft=max(2^(nextpow2(N)+pad),N); % number of points in fft of prolates
    0069 [f,findx]=getfgrid(Fs,nfft,fpass); % get frequency grid for evaluation
    0070 tapers=dpsschk(tapers,N,Fs); % check tapers
    0071 K=size(tapers,2);
    0072 J=mtfftpt(data,tapers,nfft,t,f,findx); % mt fft for point process times
    0073 A=sqrt(1:K-1);
    0074 A=repmat(A,[size(J,1) 1]);
    0075 A=repmat(A,[1 1 size(J,3)]);
    0076 S=squeeze(mean(J(:,1:K-1,:).*A.*conj(J(:,2:K,:)),2));
    0077 if trialave; S=squeeze(mean(S,2));end;
    0078 nphi=length(phi);
    0079 for p=1:nphi;
    0080     dS(p,:,:)=real(exp(i*phi(p))*S);
    0081 end;
    0082 dS=squeeze(dS);
    0083 dS=change_row_to_column(dS);