# mtspectrumc

## PURPOSE

Multi-taper spectrum - continuous process

## SYNOPSIS

function [S,f,Serr]=mtspectrumc(data,params)

## DESCRIPTION

     Multi-taper spectrum - continuous process

     Usage:

     [S,f,Serr]=mtspectrumc(data,params)
     Input:
     Note units have to be consistent. See chronux.m for more information.
           data (in form samples x channels/trials) -- required
           params: structure with fields tapers, pad, Fs, fpass, err, 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
               err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
                                       [0 p] or 0 - no error bars) - optional. Default 0.
               trialave (average over trials/channels when 1, don't average when 0) - optional. Default 0
     Output:
           S       (spectrum in form frequency x channels/trials if trialave=0;
                   in the form frequency if trialave=1)
           f       (frequencies)
           Serr    (error bars) only for err(1)>=1

## 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
- specerr Function to compute lower and upper confidence intervals on the spectrum

This function is called by:

- ftestc computes the F-statistic for sine wave in locally-white noise (continuous data).
- mtspecgramc Multi-taper time-frequency spectrum - continuous process
- mtspectrum_of_spectrumc Multi-taper segmented, second spectrum (spectrum of the log spectrum) for a continuous process
- mtspectrumtrigc Multi-taper event triggered time-frequency spectrum - continuous process
- rmlinesc removes significant sine waves from data (continuous data).
- mtspecgramc_slow Multi-taper time-frequency spectrum - continuous process
- testAvg3 This is a calling routine to test & check out the power spectrum &
- testAvg4 This is a calling routine to test & check out the power spectrum &
- testscript function testscript(pname,direction,movingwin,segave,params,fscorr)

## SOURCE CODE

    0001 function [S,f,Serr]=mtspectrumc(data,params)
    0002 % Multi-taper spectrum - continuous process
    0003 %
    0004 % Usage:
    0005 %
    0006 % [S,f,Serr]=mtspectrumc(data,params)
    0007 % Input:
    0008 % Note units have to be consistent. See chronux.m for more information.
    0009 %       data (in form samples x channels/trials) -- required
    0010 %       params: structure with fields tapers, pad, Fs, fpass, err, trialave
    0011 %       -optional
    0012 %           tapers : precalculated tapers from dpss or in the one of the following
    0013 %                    forms:
    0014 %                    (1) A numeric vector [TW K] where TW is the
    0015 %                        time-bandwidth product and K is the number of
    0016 %                        tapers to be used (less than or equal to
    0017 %                        2TW-1).
    0018 %                    (2) A numeric vector [W T p] where W is the
    0019 %                        bandwidth, T is the duration of the data and p
    0020 %                        is an integer such that 2TW-p tapers are used. In
    0021 %                        this form there is no default i.e. to specify
    0022 %                        the bandwidth, you have to specify T and p as
    0023 %                        well. Note that the units of W and T have to be
    0024 %                        consistent: if W is in Hz, T must be in seconds
    0025 %                        and vice versa. Note that these units must also
    0026 %                        be consistent with the units of params.Fs: W can
    0027 %                        be in Hz if and only if params.Fs is in Hz.
    0028 %                        The default is to use form 1 with TW=3 and K=5
    0029 %
    0030 %            pad            (padding factor for the FFT) - optional (can take values -1,0,1,2...).
    0031 %                    -1 corresponds to no padding, 0 corresponds to padding
    0032 %                    to the next highest power of 2 etc.
    0033 %                       e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT
    0034 %                       to 512 points, if pad=1, we pad to 1024 points etc.
    0035 %                       Defaults to 0.
    0036 %           Fs   (sampling frequency) - optional. Default 1.
    0037 %           fpass    (frequency band to be used in the calculation in the form
    0038 %                                   [fmin fmax])- optional.
    0039 %                                   Default all frequencies between 0 and Fs/2
    0040 %           err  (error calculation [1 p] - Theoretical error bars; [2 p] - Jackknife error bars
    0041 %                                   [0 p] or 0 - no error bars) - optional. Default 0.
    0042 %           trialave (average over trials/channels when 1, don't average when 0) - optional. Default 0
    0043 % Output:
    0044 %       S       (spectrum in form frequency x channels/trials if trialave=0;
    0045 %               in the form frequency if trialave=1)
    0046 %       f       (frequencies)
    0047 %       Serr    (error bars) only for err(1)>=1
    0048
    0049 if nargin < 1; error('Need data'); end;
    0050 if nargin < 2; params=[]; end;
    0051 [tapers,pad,Fs,fpass,err,trialave,params]=getparams(params);
    0052 if nargout > 2 && err(1)==0;
    0053 %   Cannot compute error bars with err(1)=0. Change params and run again.
    0054     error('When Serr is desired, err(1) has to be non-zero.');
    0055 end;
    0056 data=change_row_to_column(data);
    0057 N=size(data,1);
    0058 nfft=max(2^(nextpow2(N)+pad),N);
    0059 [f,findx]=getfgrid(Fs,nfft,fpass);
    0060 tapers=dpsschk(tapers,N,Fs); % check tapers
    0061 J=mtfftc(data,tapers,nfft,Fs);
    0062 J=J(findx,:,:);
    0063 S=squeeze(mean(conj(J).*J,2));
    0064 if trialave; S=squeeze(mean(S,2));end;
    0065 if nargout==3;
    0066    Serr=specerr(S,J,err,trialave);
    0067 end;