Interlace is the method to create a new data stream from two data streams, each of which has a constant time interval sequence. Formally, suppose $A = (a , \Delta_{a} )$ and $B = (b, \Delta_{b})$ are two data streams, each have a constant time sequence. For convenience, we use $\Delta_{a}$ and $\Delta_{b}$ to also denote the constant terms of each of those sequences. We construct a new data stream $C = (c, \Delta_{c})$ , also having constant time interval, as follows:

Deinterlace is the method of constructing two data streams , $A$ and $B$ , each having constant time interval, from a given data stream $C$ and primary interlace value $\Delta $ of computed stream, where $C$ has constant time interval.

$ a_{n} = c_{n+ \left\lceil \frac{(n+1)\Delta _{a}}{\Delta _{b}} \right\rceil }\ ,\ \Delta _{a}=\frac{\Delta _{c}\Delta _{b}}{\left\vert \Delta _{c}-\Delta _{b}\right\vert } \label{deinterlace_a} $ and $ b_{n} = c_{n+\left\lfloor \frac{n\Delta _{b}}{\Delta _{a}}\right\rfloor} ,\ \Delta _{b}=\frac{\Delta _{c}\Delta _{a}}{\left\vert \Delta _{c}-\Delta_{a}\right\vert } \label{deintrlace_b} $

This sequences are the Fraenkel partition theorem instance.

References

[1]

Aviezri S. Fraenkel, The bracket function and complementary sets of integers, Canad. J. Math. 21 (1969), 6-27. MR 38:3214

[2]

Michal Widera, Deterministic method of data sequence processing, Vol. IV, ISSN 1732-1360, Annales UMCS (2006), 314-331. UMCS Annales AI