Given $j, n, t$ are the decomposition level,
oscillation index, and time index, respectively, the MODWPT is given by
$$\widetilde{W}_{j,n,t} \equiv \sum_{l=0}^{L-1}\widetilde{u}_{n,l}
\widetilde{W}_{j-1,\lfloor n/2 \rfloor, t - 2^{j-1}\;l \mbox{ mod }N}$$The variable $L$ is the length of the filters defined by
$$\widetilde{u}_{n,l} \equiv \left{
\begin{array}{ll}
\widetilde{g_l}/\surd{2}, & \mbox{ if }n \bmod 4=0 \mbox{ or }3; \
\widetilde{h_l}/\surd{2}, & \mbox{ if }n \bmod 4=1 \mbox{ or }2,
\end{array}\right.$$
where $g$ and $h$ are the scaling filter and wavelet filter, respectively.
By definition, $\widetilde{W}_{0,0,t} \equiv X_t$ where
${X_t}$ is the original time series.