PlanetMath: stream interlace and deinterlace

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stream interlace and deinterlace

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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:

$\begin{displaymath} c_{n}=\left\{ \begin{array}{cc} b_{n-\left\lfloor n z \right... ...ta _{c}= \frac{\Delta _{a}\Delta _{b}}{\Delta _{a}+\Delta _{b}}\end{displaymath}$

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

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

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

"stream interlace and deinterlace" is owned by michal.

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Other names:

interlace deinterlace

Also defines:

stream junction method

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Cross-references: integers, complementary, bracket function, references, Fraenkel partition theorem, primary, constant terms, sequence, interval, data stream

This is version 13 of stream interlace and deinterlace, born on 2005-12-27, modified 2007-06-23.
Object id is 7543, canonical name is WideraInterlaceAndDeinterlace.
Accessed 9420 times total.

Classification:

AMS MSC:

11B83 (Number theory :: Sequences and sets :: Special sequences and polynomials)

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