Ladder Wave Digital Filters is a class of IIR digital filters derived from double resistively terminated ladder networks, which gives them good stability and low sensitivity to variations in the element values. An approach to design maximally fast bit-serial ladder wave digital filters is presented based on the numerically equivalent state-space representation of the signal-flow graph. An algor...

Suppose $X$ is a simple graph. The $X-$join $Gamma$ of a set ofcomplete or empty graphs ${X_x }_{x in V(X)}$ is a simple graph with the following vertex and edge sets:begin{eqnarray*}V(Gamma) &=& {(x,y) | x in V(X) & y inV(X_x) },\ E(Gamma) &=& {(x,y)(x^prime,y^prime) | xx^prime in E(X) or else x = x^prime & yy^prime in E(X_x)}.end{eqnarray*}The $X-$join graph $Gamma$ is said to be re...

Let $\mathcal{F}=\{F_{\alpha}: \alpha\in \mathcal{A}\}$ be a family of infinite graphs, together with $\Lambda$. The Factorization Problem $FP(\mathcal{F}, \Lambda)$ asks whether $\mathcal{F}$ can realized as factorization $\Lambda$, namely, there is $\mathcal{G}=\{\Gamma_{\alpha}: $\Lambda$ such that each $\Gamma_{\alpha}$ copy $F_{\alpha}$.We study this problem when either the Rado graph $R$ ...