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Homestream interlace and deinterlace
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stream interlace and deinterlace
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:
$c_{{n}}=\left\{\begin{array}[]{cc}b_{{n\left\lfloor nz\right\rfloor}}&\left% \lfloor nz\right\rfloor=\left\lfloor\left(n+1\right)z\right\rfloor\\ a_{{\left\lfloor nz\right\rfloor}}&\left\lfloor nz\right\rfloor\neq\left% \lfloor\left(n+1\right)z\right\rfloor\end{array}\right.,z=\frac{\Delta_{{b}}}{% \Delta_{{a}}+\Delta_{{b}}},\Delta_{{c}}=\frac{\Delta_{{a}}\Delta_{{b}}}{\Delta% _{{a}}+\Delta_{{b}}}$
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.
$a_{{n}}=c_{{n+\left\lceil\frac{(n+1)\Delta_{{a}}}{\Delta_{{b}}}\right\rceil}}% \ ,\ \Delta_{{a}}=\frac{\Delta_{{c}}\Delta_{{b}}}{\left\Delta_{{c}}\Delta_{{% b}}\right}$ and $b_{{n}}=c_{{n+\left\lfloor\frac{n\Delta_{{b}}}{\Delta_{{a}}}\right\rfloor}},\ % \Delta_{{b}}=\frac{\Delta_{{c}}\Delta_{{a}}}{\left\Delta_{{c}}\Delta_{{a}}% \right}$
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 17321360, Annales UMCS (2006), 314–331. UMCS Annales AI
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