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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. figurea