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Table 1 A schematic representation of the t-CWT algorithm as implemented by the software [16, 17]

From: Multivariate assessment of event-related potentials with the t-CWT method

t-CWT

Input

Processing

Output

Function

Files

Steps

Files: variables (equations)

prm2mat

input parameter file

Computes time-to-frequency domain transformation matrix, CWT matrix and log-grid matrix

_A_const.mat : \(\tilde{\mathbf {T}}_{\mathbf {f}}\) (2229), \(\tilde{\mathbf {T}}_{\mathbf {w}}\) (1618, 4345), \((s^g,t^{g,h})\) (4041)

t2f

* .t.mat

Performs time-to-frequency domain transformation and filtering of ERP datasets

* .f.mat : \(\tilde{\mathbf {V}}\!_{\mathbf {f}}\) (28)

 

_A_const.mat

 

* .ri0.mat : initial index vector

f2pc

* .f.mat

Computes PCT by performing PCA-based multivariate outlier detection in frequency domain

* .pc.mat : \({\hat{\mathbf {T}}}_{\mathbf {p}}\) (3338)

 

* .ri0.mat

 

* .ri1.mat : outlier index vector

f2cwss

* .f.mat

Performs CWT and computes sums of squares (SS) for Student’s t-values for t-CWT scalograms

* .cwss.mat : SS of \({\tilde{\mathbf {W}}}\) (48) for the computation of \(\sigma ^k_{{\!\!_\mathcal {A}}{\!_\mathcal {B}}}(s,t)\) and \(\mathtt {t}^k(s,t)\) (19)

 

* .pc.mat

  
 

* .ri1.mat

  
 

_A_const.mat

  

pc2cnd2ri

* .f.mat

Performs outlier detection for each experimental condition separately with fixed PCT obtained by f2pc

* .ri2.mat : outlier index vector

 

* .pc.mat

  
 

* .ri1.mat

  

f2x

* .f.mat

Computes t-CWT scalograms using SS computed by f2cwss, detects t-CWT scalogram extrema, and computes t-CWT matrix

* .tcw.mat : \(\mathtt {t}^k(s,t)\) (19)

 

* .pc.mat

 

* .x.mat : \(\tilde{\mathbf {T}}^\star _{\mathbf {w}}\) (49)

 

* .cwss.mat

  
 

* .ri2.mat

  
 

_A_const.mat

  

x2ld

* .f.mat

Performs PCA-based step-down reduction of t-CWT features obtained by f2x and computes LDF in reduced feature space

* .ld.mat : \({\hat{\mathbf {T}}}^{\mathbf {\star }}_{\mathbf {p}}\) (5051), \(\mathbf {d_f^\star }\) (5255)

 

* .x.mat

  
 

* .ri2.mat

  
  1. The full names of the functions include the prefix ‘tcwt_’ (e.g., ‘tcwt_t2f’). The functions listed above (except for prm2mat) operate according to the following general scheme:
  2. figure a