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)

- minmaxsptimes Find the minimum and maximum of the spike times in each channel
- mtfftpt Multi-taper fourier transform for point process given as times

- mtdspecgrampt Multi-taper derivative time-frequency spectrum - point process times

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);

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