Читать книгу EEG Signal Processing and Machine Learning - Saeid Sanei - Страница 69

Different waveforms/wavelets/kernels have been defined for the continuous WTs. The most popular ones are given below.

Morlet's wavelet is a complex waveform defined as:

(4.25)

This wavelet may be decomposed into its constituent real and imaginary parts as:

(4.26)

(4.27)

where b₀ is a constant, and it is considered that b₀ > 0 to satisfy the admissibility condition. Figure 4.5 shows respectively the real and imaginary parts.

The Mexican hat defined by Murenzi [17] is:

(4.28)

which is the second derivative of a Gaussian waveform (see Figure 4.6).