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)

- mtfftc Multi-taper fourier transform - continuous data

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

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);

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