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Mon Aug 29 23:46:13 EDT 2016

## Packetized TDM as coordinate transformations

```For lack of better name, packetized TDM meaning: to transmit a number
of channels in block form, e.g. N samples from channel 0, followed by
N from channel 1.

Just a practical format I ran into, but this is to hint at the general
idea of chunking which tends to happen in nested form and can get
confusion.  Therefore it makes sense to look at TDM as coordinate
transformations

An important thing to realize is that this form of TDM can be seen as
a 2-step process: the introduction of an extra dimension followed by
the removal of another:

1) packetize: splitting t into a 2-dimensional (p,i) coordinate
2) multiplex: flattening (c,p) into a 1-dimensional p' coordinate

(c,t)    // channel(finite), time(infinite)

<->

(c,p,i)  // channel(finite), index(finite), packet(infinite)

<->

(p',i)  //  index(finite), flattened packet+channel (infinite)

p  = t div N
i  = t mod N
p' = p * N + i

c = p mod N
t = p * N + i
p = (p' - i) div N

```
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