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This paper deals with structural properties of a class of asymptotic filters from the filter banks design point of view. It is shown that both, the continuousand discrete-time lattice filter structures can be derived as a natural consequence of strict causality, minimality and asymptotic stability requirements. An abstract form of classic Tellegen’s relation is introduced and used as a basic design tool expressing the signal energy conservation law for filter state space representations. It is demonstrated that in discrete-time version the resulting asymptotic filter bank structure contains the well known direct FIR filter structure as special case. Key-Words: Asymptotic filter, continuous filter, digital filter, energy function, filter bank, Lattice structure, Tellegen’s theorem, wavelets filters.