stream interlace and deinterlace

Interlace is the method to create a new data stream fromtwo 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 termsof each of those sequences. We construct a new data stream $C=(c,\\Delta_{c})$ , also having constant time interval, as follows:

$c_{n}=\\left\\{\\begin{array}[]{cc}b_{n-\\left\\lfloor nz\\right\\rfloor}&\\left%\\lfloor nz\\right\\rfloor=\\left\\lfloor\\left(n+1\\right)z\\right\\rfloor\\\\a_{\\left\\lfloor nz\\right\\rfloor}&\\left\\lfloor nz\\right\\rfloor\eq\\left\\lfloor%\\left(n+1\\right)z\\right\\rfloor\\end{array}\\right.,z=\\frac{\\Delta_{b}}{\\Delta_{a%}+\\Delta_{b}},\\Delta_{c}=\\frac{\\Delta_{a}\\Delta_{b}}{\\Delta_{a}+\\Delta_{b}}$

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. http://www.ams.org/mathscinet-getitem?mr=38:3214MR38:3214
[2: ] Michal Widera, Deterministic method of data sequence processing, Vol. IV, ISSN 1732-1360, Annales UMCS (2006), 314–331. http://www.annales.umcs.lublin.pl/AI/index.htmlUMCS Annales AI

单词	StreamInterlaceAndDeinterlace
释义	stream interlace and deinterlace Interlace is the method to create a new data stream fromtwo 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 termsof each of those sequences. We construct a new data stream $C=(c,\\Delta_{c})$ , also having constant time interval, as follows: $c_{n}=\\left\\{\\begin{array}[]{cc}b_{n-\\left\\lfloor nz\\right\\rfloor}&\\left%\\lfloor nz\\right\\rfloor=\\left\\lfloor\\left(n+1\\right)z\\right\\rfloor\\\\a_{\\left\\lfloor nz\\right\\rfloor}&\\left\\lfloor nz\\right\\rfloor\eq\\left\\lfloor%\\left(n+1\\right)z\\right\\rfloor\\end{array}\\right.,z=\\frac{\\Delta_{b}}{\\Delta_{a%}+\\Delta_{b}},\\Delta_{c}=\\frac{\\Delta_{a}\\Delta_{b}}{\\Delta_{a}+\\Delta_{b}}$ 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. http://www.ams.org/mathscinet-getitem?mr=38:3214MR38:3214 [2 ] Michal Widera, Deterministic method of data sequence processing, Vol. IV, ISSN 1732-1360, Annales UMCS (2006), 314–331. http://www.annales.umcs.lublin.pl/AI/index.htmlUMCS Annales AI
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