# mtdspectrumc

## PURPOSE

Multi-taper frequency derivative of the spectrum - continuous process

## SYNOPSIS

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

## DESCRIPTION

     Multi-taper frequency derivative of the spectrum - continuous process

     Usage:

     [dS,f]=mtdspectrumc(data,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
           phi         (angle for evaluation of derivative) -- required.
                           e.g. phi=[0,pi/2] gives 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/channels when 1, don't average when 0) - optional. Default 0
     Output:
           dS       (spectral derivative in form phi x frequency x channels/trials if trialave=0 or
                    in form phi x frequency if trialave=1)
           f        (frequencies)

## CROSS-REFERENCE INFORMATION

This function calls:

- 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

This function is called by:

- mtdspecgramc Multi-taper derivative of the time-frequency spectrum - continuous process
- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [dS,f]=mtdspectrumc(data,phi,params)
    0002 % Multi-taper frequency derivative of the spectrum - continuous process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [dS,f]=mtdspectrumc(data,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 %       data        (in form samples x channels/trials or a single vector) -- required
    0013 %       phi         (angle for evaluation of derivative) -- required.
    0014 %                       e.g. phi=[0,pi/2] gives the time and frequency derivatives
    0015 %       params: structure with fields tapers, pad, Fs, fpass, trialave
    0016 %       - optional
    0017 %           tapers : precalculated tapers from dpss or in the one of the following
    0018 %                    forms:
    0019 %                   (1) A numeric vector [TW K] where TW is the
    0020 %                       time-bandwidth product and K is the number of
    0021 %                       tapers to be used (less than or equal to
    0022 %                       2TW-1).
    0023 %                   (2) A numeric vector [W T p] where W is the
    0024 %                       bandwidth, T is the duration of the data and p
    0025 %                       is an integer such that 2TW-p tapers are used. In
    0026 %                       this form there is no default i.e. to specify
    0027 %                       the bandwidth, you have to specify T and p as
    0028 %                       well. Note that the units of W and T have to be
    0029 %                       consistent: if W is in Hz, T must be in seconds
    0030 %                       and vice versa. Note that these units must also
    0031 %                       be consistent with the units of params.Fs: W can
    0032 %                       be in Hz if and only if params.Fs is in Hz.
    0033 %                       The default is to use form 1 with TW=3 and K=5
    0034 %
    0035 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0036 %                    -1 corresponds to no padding, 0 corresponds to padding
    0037 %                    to the next highest power of 2 etc.
    0038 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0039 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0040 %                       Defaults to 0.
    0041 %           Fs   (sampling frequency) - optional. Default 1.
    0042 %           fpass    (frequency band to be used in the calculation in the form
    0043 %                                   [fmin fmax])- optional.
    0044 %                                   Default all frequencies between 0 and Fs/2
    0045 %           trialave (average over trials/channels when 1, don't average when 0) - optional. Default 0
    0046 % Output:
    0047 %       dS       (spectral derivative in form phi x frequency x channels/trials if trialave=0 or
    0048 %                in form phi x frequency if trialave=1)
    0049 %       f        (frequencies)
    0050
    0051 if nargin < 2; error('Need data and angle'); end;
    0052 if nargin < 3; params=[]; end;
    0053 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0054 clear err params
    0055 data=change_row_to_column(data);
    0056 N=size(data,1);
    0057 nfft=max(2^(nextpow2(N)+pad),N);
    0058 [f,findx]=getfgrid(Fs,nfft,fpass);
    0059 tapers=dpsschk(tapers,N,Fs); % check tapers
    0060 K=size(tapers,2);
    0061 J=mtfftc(data,tapers,nfft,Fs);
    0062 J=J(findx,:,:);
    0063 A=sqrt(1:K-1);
    0064 A=repmat(A,[size(J,1) 1]);
    0065 A=repmat(A,[1 1 size(J,3)]);
    0066 S=squeeze(mean(J(:,1:K-1,:).*A.*conj(J(:,2:K,:)),2));
    0067 if trialave; S=squeeze(mean(S,2));end;
    0068 nphi=length(phi);
    0069 for p=1:nphi;
    0070     dS(p,:,:)=real(exp(i*phi(p))*S);
    0071 end;
    0072 dS=squeeze(dS);
    0073 dS=change_row_to_column(dS);