9 problems

Let $\mathbf{R}$ be a Hermitian positive-definite matrix arising from a broad class of physical signal models, and let $\mathcal{B}$ be a basis. Let…

Let $\mathcal{F} \in \mathbb{C}^{m \times p \times n}$ be a signal, let $\Psi$ denote its samples under the stated tensor-product dynamical evolution, and let…

Optimal reproducing-filter norm conjecture. Every $s$-dimensional SIS admits a reproducing filter $\varphi\in\mathbb{C}_n(\mathbb{Z})$ such that

Near second-order Markov conjecture. The MA filtering of the first-order Markov process generates nearly a second-order Markov process.

Let $F$ be a scalable frame with minimal scalings v_j_{j\in I}, and let $J\subset I$ be inclusion-minimal subject to … Suppose that … is the smallest orthogonal partition of…

Let $\{t_k\}_{k\in\mathbb{Z}}\subset\mathbb{R}$ be an ordered complete interpolating sequence for $\mathcal{PW}_{\pi}^{2}$. Logarithmic lower-bound conjecture. There exists a posit…

Let $\{t_k\}_{k\in\mathbb{Z}}\subset\mathbb{R}$ be an ordered complete interpolating sequence for $\mathcal{PW}_{\pi}^{2}$, let $\phi_k$ be as defined in the source, and let…

Let t_k_{k\in\mathbb{Z}}\subset\mathbb{R} be an ordered complete interpolating sequence for $\mathcal{PW}_{\pi}^{2}$, let $\phi_k$ be as defined in the source, and let…

Counting-length conjecture. Generically, a length-$m_v$ FIR synthesis bank achieving perfect reconstruction exists if and only if