# mtdspecgramc

## PURPOSE

Multi-taper derivative of the time-frequency spectrum - continuous process

## SYNOPSIS

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

## DESCRIPTION

     Multi-taper derivative of the time-frequency spectrum - continuous process

     Usage:

     [dS,t,f]=mtdspecgramc(data,movingwin,phi,params)
     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        (in form samples x channels/trials or a single vector) -- required
           movingwin         (in the form [window winstep] i.e length of moving
                                                     window and step size.
                                                     Note that units here have
                                                     to be consistent with
                                                     units of Fs - 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
                         Note that T has to be equal to movingwin(1).

                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/channels when 1, don't average when 0) - optional. Default 0
     Output:
           dS      (spectral derivative in form phi x time x frequency x channels/trials if trialave=0;
                   in form phi x time x frequency if trialave=1)
           t       (times)
           f       (frequencies)

## CROSS-REFERENCE INFORMATION

This function calls:

- mtdspectrumc Multi-taper frequency derivative of the spectrum - continuous process
- 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

This function is called by:

- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)
- classify_spectra CLASSIFY_SPECTRA M-file for classify_spectra.fig
- wave_browser WAVE_BROWSER M-file for wave_browser.fig

## SOURCE CODE

    0001 function [dS,t,f]=mtdspecgramc(data,movingwin,phi,params)
    0002 % Multi-taper derivative of the time-frequency spectrum - continuous process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [dS,t,f]=mtdspecgramc(data,movingwin,phi,params)
    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 %
    0013 %       data        (in form samples x channels/trials or a single vector) -- required
    0014 %       movingwin         (in the form [window winstep] i.e length of moving
    0015 %                                                 window and step size.
    0016 %                                                 Note that units here have
    0017 %                                                 to be consistent with
    0018 %                                                 units of Fs - required
    0019 %       phi         (angle for evaluation of derivative) -- required
    0020 %                       e.g. phi=[0,pi/2] giving the time and frequency
    0021 %                       derivatives
    0022 %       params: structure with fields tapers, pad, Fs, fpass, trialave
    0023 %       -optional
    0024 %           tapers : precalculated tapers from dpss or in the one of the following
    0025 %                    forms:
    0026 %                    (1) A numeric vector [TW K] where TW is the
    0027 %                        time-bandwidth product and K is the number of
    0028 %                        tapers to be used (less than or equal to
    0029 %                        2TW-1).
    0030 %                    (2) A numeric vector [W T p] where W is the
    0031 %                        bandwidth, T is the duration of the data and p
    0032 %                        is an integer such that 2TW-p tapers are used. In
    0033 %                        this form there is no default i.e. to specify
    0034 %                        the bandwidth, you have to specify T and p as
    0035 %                        well. Note that the units of W and T have to be
    0036 %                        consistent: if W is in Hz, T must be in seconds
    0037 %                        and vice versa. Note that these units must also
    0038 %                        be consistent with the units of params.Fs: W can
    0039 %                        be in Hz if and only if params.Fs is in Hz.
    0040 %                        The default is to use form 1 with TW=3 and K=5
    0041 %                     Note that T has to be equal to movingwin(1).
    0042 %
    0043 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0044 %                    -1 corresponds to no padding, 0 corresponds to padding
    0045 %                    to the next highest power of 2 etc.
    0046 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0047 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0048 %                       Defaults to 0.
    0049 %           Fs   (sampling frequency) - optional. Default 1.
    0050 %           fpass    (frequency band to be used in the calculation in the form
    0051 %                                   [fmin fmax])- optional.
    0052 %                                   Default all frequencies between 0 and Fs/2
    0053 %           trialave - (average over trials/channels when 1, don't average when 0) - optional. Default 0
    0054 % Output:
    0055 %       dS      (spectral derivative in form phi x time x frequency x channels/trials if trialave=0;
    0056 %               in form phi x time x frequency if trialave=1)
    0057 %       t       (times)
    0058 %       f       (frequencies)
    0059
    0060 if nargin < 3; error('Need data, window parameters and angle'); end;
    0061 if nargin < 4; params=[]; end;
    0062
    0063 if length(params.tapers)==3 & movingwin(1)~=params.tapers(2);
    0064     error('Duration of data in params.tapers is inconsistent with movingwin(1), modify params.tapers(2) to proceed')
    0065 end
    0066
    0067 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0068 clear err
    0069 data=change_row_to_column(data);
    0070 [N,C]=size(data);
    0071 Nwin=round(Fs*movingwin(1)); % number of samples in window
    0072 Nstep=round(movingwin(2)*Fs); % number of samples to step through
    0073 nfft=max(2^(nextpow2(Nwin)+pad),Nwin);
    0074 f=getfgrid(Fs,nfft,fpass); Nf=length(f);
    0075 params.tapers=dpsschk(tapers,Nwin,Fs); % check tapers
    0076 params.tapers=tapers;
    0077 winstart=1:Nstep:N-Nwin+1;
    0078 nw=length(winstart);
    0079 if trialave==0; dS=zeros(length(phi),nw,Nf,C); else dS=zeros(length(phi),nw,Nf); end;
    0080 for n=1:nw;
    0081    indx=winstart(n):winstart(n)+Nwin-1;
    0082    datawin=data(indx,:);
    0083    [ds,f]=mtdspectrumc(datawin,phi,params);
    0084    dS(:,n,:,:)=ds;
    0085 end;
    0086 dS=squeeze(dS);
    0087 sz=size(dS);
    0088 % if length(sz)==3;
    0089 %    dS=permute(dS,[2 1 3 4]);
    0090 % elseif length(phi)>1
    0091 %    dS=permute(dS,[2 1 3]);
    0092 % end;
    0093 winmid=winstart+round(Nwin/2);
    0094 t=winmid/Fs;