This library performs time-frequency analysis (mostly using the multi-taper spectral estimation method) of univariate and multivariate data, both for continuous processes such as LFP/EEG and for point processes such as spike times. Point process can either be stored as times or as a binned process of counts. The routines in this library are named differently for the three cases. For calculations that can be performed for each of the three data types, we use suffixes c, pb, or pt to refer to continuous, point process binned counts, or point process times. For example, the spectrum calculation is performed mtspectrumc for continuous processes, mtspectrumpb for a binned point process, and mtspectrumpt for a point process consisting of times. There are also routines for calculating hybrid quantities involving one continuous and one point process. These are suffixed in a similar manner. For example, coherencycpb calculates the coherency between a binned point process and a continuous process. Certain variables are used repeatedly in this library. DATA data in most cases can be univariate or multivariate, and either point process, or continuous. Continuous data: Continuous data is assumed to be a matrix with dimensions samples x channels/trials. Point Process: A single time series of spike times can be in the form of a column vector. Multichannel/trial spike time data is not amenable to this storage format, since there are generally different number of spikes in each channel/trial. Instead, multichannel/trial spike data is stored in a structure array. A structure is a matlab data object with various fields. These fields contain the elements e.g. The command data=struct('times',[]); creates an empty structure with field 'times'. Similarly, the command data=struct('times',[1 2 3]); creates the structure with the field 'times' containing integers 1, 2, and 3. We can also have a structure array (or an array of structures) defined for example, by data(1)=struct('times',rand(1,100)); and data(2)=struct('times',rand(1,200)); This is a 2 dimensional structure array where the first field is a 100 dimensional random vector, and the second field is a 200 dimensional random vector. This format allows storage of multichannel point process times in a single variable data. The above holds for point processes stored as times. If instead, the point processes are binned, then one can use a matrix to represent them Summary: data - array of continuous data with dimensions time x channels structural array of spike times with dimensions equal to the number of channels 1d array of spike times as a column vector array of binned spike counts with dimensions time x channels PARAMETERS: These are various parameters used in the spectral calculations. Since these parameters are used by most routines in Chronux, they are stored in a single structure params. The fields of params are 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: frequencies in an fft calculation can range from 0 to Fs/2 where Fs is the sampling frequency. Sometimes it may be useful to compute fourier transforms (and resulting quantities like the spectrum over a smaller range of frequencies). This is specified by fpass, which can be in the form [fmin fmax] where fmin >=0 and fmax<=Fs/2. optional (default [0 Fs/2]) err=[errtype p] calculates theoretical error bars (confidence levels) when errtype=1 and jackknife error bars when errchk=2. In each case, the error is calculated at a p value specified by p. - optional (default 0) trialave: trialave controls whether or not to average over channels/trials for multichannel/trial analyses. trialave=0 (default) implies no trial averaging, trialave=1 implies that the quantity of interest is averaged over channels/trials. optional (default 0) Other parameters are discussed in individual routines as and when they are used.

0001 function chronux 0002 % This library performs time-frequency analysis (mostly using the 0003 % multi-taper spectral estimation method) of univariate and multivariate 0004 % data, both for continuous processes such as LFP/EEG and for point 0005 % processes such as spike times. Point process can either be stored as 0006 % times or as a binned process of counts. The routines in this library 0007 % are named differently for the three cases. For calculations 0008 % that can be performed for each of the three data types, we use suffixes 0009 % c, pb, or pt to refer to continuous, point process binned counts, or 0010 % point process times. For example, the spectrum calculation is performed 0011 % mtspectrumc for continuous processes, mtspectrumpb for a binned point 0012 % process, and mtspectrumpt for a point process consisting of times. There 0013 % are also routines for calculating hybrid quantities involving one continuous 0014 % and one point process. These are suffixed in a similar manner. For 0015 % example, coherencycpb calculates the coherency between a binned point process 0016 % and a continuous process. 0017 % 0018 % Certain variables are used repeatedly in this library. 0019 % 0020 % DATA 0021 % data in most cases can be univariate or multivariate, and either point process, 0022 % or continuous. 0023 % 0024 % Continuous data: Continuous data is assumed to be a matrix with 0025 % dimensions samples x channels/trials. 0026 % 0027 % Point Process: A single time series of spike times can be in the form of 0028 % a column vector. 0029 % Multichannel/trial spike time data is not amenable to this 0030 % storage format, since there are generally different 0031 % number of spikes in each channel/trial. Instead, 0032 % multichannel/trial spike data is stored in a structure 0033 % array. A structure is a matlab data object with various 0034 % fields. These fields contain the elements 0035 % e.g. The command data=struct('times',[]); creates an empty 0036 % structure with field 'times'. Similarly, the command 0037 % data=struct('times',[1 2 3]); creates the structure with 0038 % the field 'times' containing integers 1, 2, and 3. 0039 % 0040 % We can also have a structure array (or an array of structures) 0041 % defined for example, by 0042 % data(1)=struct('times',rand(1,100)); and 0043 % data(2)=struct('times',rand(1,200)); 0044 % This is a 2 dimensional structure array where the 0045 % first field is a 100 dimensional random vector, and 0046 % the second field is a 200 dimensional random vector. 0047 % This format allows storage of multichannel point 0048 % process times in a single variable data. 0049 % 0050 % The above holds for point processes stored as times. 0051 % If instead, the point processes are binned, then one 0052 % can use a matrix to represent them 0053 % 0054 % 0055 % Summary: data - array of continuous data with dimensions time x channels 0056 % structural array of spike times with dimensions 0057 % equal to the number of channels 0058 % 1d array of spike times as a column vector 0059 % array of binned spike counts with dimensions time x channels 0060 % 0061 % PARAMETERS: 0062 % These are various parameters used in the spectral calculations. Since 0063 % these parameters are used by most routines in Chronux, they are stored in 0064 % a single structure params. The fields of params are 0065 % 0066 % tapers : precalculated tapers from dpss or in the one of the following 0067 % forms: 0068 % (1) A numeric vector [TW K] where TW is the 0069 % time-bandwidth product and K is the number of 0070 % tapers to be used (less than or equal to 0071 % 2TW-1). 0072 % (2) A numeric vector [W T p] where W is the 0073 % bandwidth, T is the duration of the data and p 0074 % is an integer such that 2TW-p tapers are used. In 0075 % this form there is no default i.e. to specify 0076 % the bandwidth, you have to specify T and p as 0077 % well. Note that the units of W and T have to be 0078 % consistent: if W is in Hz, T must be in seconds 0079 % and vice versa. Note that these units must also 0080 % be consistent with the units of params.Fs: W can 0081 % be in Hz if and only if params.Fs is in Hz. 0082 % The default is to use form 1 with TW=3 and K=5 0083 % 0084 % 0085 % pad: (padding factor for the FFT) - optional (can take values -1,0,1,2...). 0086 % -1 corresponds to no padding, 0 corresponds to padding 0087 % to the next highest power of 2 etc. 0088 % e.g. For N = 500, if PAD = -1, we do not pad; if PAD = 0, we pad the FFT 0089 % to 512 points, if pad=1, we pad to 1024 points etc. 0090 % Defaults to 0. 0091 % 0092 % Fs:sampling frequency.optional (default 1) 0093 % 0094 % 0095 % fpass: frequencies in an fft calculation can range from 0 to Fs/2 where 0096 % Fs is the sampling frequency. Sometimes it may be useful to 0097 % compute fourier transforms (and resulting quantities like the 0098 % spectrum over a smaller range of frequencies). This is specified 0099 % by fpass, which can be in the form [fmin fmax] where fmin >=0 and 0100 % fmax<=Fs/2. optional (default [0 Fs/2]) 0101 % 0102 % err=[errtype p] calculates theoretical error bars (confidence levels) 0103 % when errtype=1 and jackknife error bars when errchk=2. In each case, the 0104 % error is calculated at a p value specified by p. - 0105 % optional (default 0) 0106 % 0107 % trialave: trialave controls whether or not to average over channels/trials for 0108 % multichannel/trial analyses. trialave=0 (default) implies no trial 0109 % averaging, trialave=1 implies that the quantity of interest is averaged 0110 % over channels/trials. optional (default 0) 0111 % 0112 % Other parameters are discussed in individual routines as and when they 0113 % are used.

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