1. In Example 7, the coefficient $\Phi_{x, 2}$ should multiply with a factor 2. That is, $\Phi_{x, 2} = 2 * (1 - \tanh(x_t)^2)$.

2. Assumption 10. 3). There should be no $\sup_{k \geq 1}$.

3. IEEE punlisher somehow messed up the notations in our manuscript in the publshed version. Speficially, many trace operators are deleted by the publisher, for example, in pp. 4643, $\sup_{k\geq 1} E[(P_k)] \leq \lambda_P$ is missing tr, and $C(P)$ is also missing a tr. Even worse, the main theorem 11 is also missing a tr around $P_0$. I have no idea why they did that, and I'm not sure if there are more errors caused by the publisher. Please find the unpublished manuscript in [tme_filter.pdf](../pdfs/tme_filter.pdf) instead.