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

This section provides a detailed, step-by-step, formal delineation of the t-CWT algorithm. In the brief intuitive descriptions published before [7], [11], most of the details were omitted. Here, a rigorous mathematical delineation of all steps is presented for the first time. Pre-processing Theoretically, the t-CWT could be performed directly in the time domain defined by (2). The CWT (16–18) is, however, highly redundant and computationally demanding. That is why the dimensionality of the vector space must be reduced substantially before computing w <img class=”mathimg” src=”http://www.biomedcentral.com/content/inline/s12868-015-0185-z-i214.gif” alt=”View MathML”/> and w ⋆ <img class=”mathimg” src=”http://www.biomedcentral.com/content/inline/s12868-015-0185-z-i215.gif” alt=”View MathML”/> (16–21). Frequency domain representation The first pre-processing step is based on a frequency domain representation of the ERPs by a discrete Fourier transform (DFT [22]; note the difference to the previous version of t-CWT [7]…


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