  In this paper we introduce the concept of super periodic potential (SPP) of
arbitrary order $n$, $n \in I^{+}$, in one dimension. General theory of wave
propagation through SPP of order $n$ is presented and the reflection and
transmission coefficients are derived in their closed analytical form by
transfer matrix formulation. We present scattering features of super periodic
rectangular potential and super periodic delta potential as special cases of
SPP. It is found that the symmetric self-similarity is the special case of
super periodicity. Thus by identifying a symmetric fractal potential as special
cases of SPP, one can obtain the tunnelling amplitude for a particle from such
fractal potential. By using the formalism of SPP we obtain the close form
expression of tunnelling amplitude of a particle for general Cantor and
Smith-Volterra-Cantor potentials.
