1. The problem is to provide the Morlet mother wavelet and the continuous wavelet transform (CWT) equations in a format suitable for copying into Word.
2. The Morlet mother wavelet is defined as:
$$\psi^{Morelet}(t) = \frac{1}{\pi^{1/4}} e^{i t \omega_0} e^{-t^2/2}$$
where $t$ is the normalized time and $\omega_0$ is the normalized frequency.
3. According to the literature, $\omega_0 = 6$ is chosen to balance time and frequency localization.
4. The continuous wavelet transform (CWT) of a time series $x$ is given by:
$$W_x(\tau, s) = \int_{-\infty}^{\infty} x(t) \tilde{\psi}_{\tau,s}^*(t) dt, \quad s, \tau \in \mathbb{R}, s \neq 0$$
where $\tilde{\psi}_{\tau,s}^*(t)$ is the complex conjugate of the scaled and translated mother wavelet.
These equations can be copied directly into Word using the equation editor with LaTeX support.
Morlet Wavelet E414A4
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.