1. The problem is to write the given wavelet transform and coherence equations in a clear, copyable format for Word. 2. The first equation defines the wavelet function: $$\tilde{\psi}_{\tau,s}(t) = \frac{1}{\sqrt{|s|}} \psi \left(\frac{t-\tau}{s}\right), \quad s,\tau \in \mathbb{R}, s \neq 0$$ This means the wavelet is scaled by $s$ and shifted by $\tau$. 3. The second equation defines the cross wavelet transform: $$w_{xy}(\tau, s) = w_x(\tau,s) w_y^{*}(\tau,s)$$ where $w_y^{*}$ is the complex conjugate of $w_y$. 4. The third expression is the power spectrum of $w_x$: $$|w_x|^{2}$$ which represents the magnitude squared of the wavelet coefficients. 5. The fourth equation defines the wavelet transform coherence: $$R_{xy}(\tau,s) = \frac{|S(W_{xy}(\tau,s))|}{\sqrt{S \left(|W_x(\tau,s)|^2\right) \cdot S \left(|W_y(\tau,s)|^2\right)}}$$ where $S$ is a smoothing operator applied to the wavelet spectra. These equations can be copied directly into Word using the equation editor with LaTeX support.