December 29, 2009
Let’s say we want to mix three channels onto two because the communication device has only two available channels but we still want to emulate a three channel link. If we can afford coding, then it’s not a problem because we can build our own protocol so add any number of channels using a structured data stream. But what if we cannot control the channel coding at all? In CDs, for example, there’s no coding: there are two channels encoded in PCM and a standard CD player wouldn’t understand the sound if it was encoded otherwise.
The solution is to mix the three channels in a quasi-reversible way, and in a way that the two channels can be listened to without much interference. One possible way is to mix the third channel is to use a phase-dependant encoding. Early “quadraphonic” audio systems did something quite similar. You can also use a plain time-domain “mixing matrix” to mix the three channels onto two. Quite expygeously, let us choose the matrix:
![M=\left[~\begin{array}{ccc} \frac{2}{3} &0&\frac{1}{3}\\ 0 &\frac{2}{3}&\frac{1}{3}\end{array}~\right]](https://s0.wp.com/latex.php?latex=M%3D%5Cleft%5B%7E%5Cbegin%7Barray%7D%7Bccc%7D+%5Cfrac%7B2%7D%7B3%7D+%260%26%5Cfrac%7B1%7D%7B3%7D%5C%5C+0+%26%5Cfrac%7B2%7D%7B3%7D%26%5Cfrac%7B1%7D%7B3%7D%5Cend%7Barray%7D%7E%5Cright%5D&bg=ffffff&fg=333333&s=0 "M=\left[~\begin{array}{ccc} \frac{2}{3} &0&\frac{1}{3}\\ 0 &\frac{2}{3}&\frac{1}{3}\end{array}~\right]")
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1 Comment | 
algorithms, data compression, Mathematics, Science, signal processing | Tagged: CD, channel mixing, least mean squares, least squares, linear algebra, linear regression, matrices, Matrix, mixing matrix, Moore-Penrose, PCM, pseudo-inverse, quadraphonic, rgb, surjection, surjective function | 
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Posted by Steven Pigeon
December 22, 2009
The other day—well, a year ago or so—I was invited to visit CBC’s digital TV studios in Montréal by the SMPTE Montréal. We were shown around, even in the somewhat small control rooms. Amongst all the displays, dials, monitors, and misc. blinkenlights, I noticed a small LCD display showing an hexagonal projection of the current show’s color gamut in 
(or maybe 
?), probably for quality assessment purposes. I thought it was pretty cool, actually.
Let’s see how we can realize this projection with as little CPU time as possible.
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1 Comment | algorithms, bit twiddling, C, embedded programming, hacks, Mathematics, programming | Tagged: animated gif, blinkenlights, camel, CBC, colorspace, digital tv, DTV, folding, folding function, gamut, gif, pairing, pairing function, real time, realtime, realtime rendering, rgb, studio, tuple, tv studio, ycrcb | Permalink
Posted by Steven Pigeon
December 18, 2009
A few days ago, I changed my machine and upgraded to Ubuntu 9.10 (Karmic Koala) and everything went fine, except for the screen-saver that would activate properly but not switch the screen into sleep mode after a while. I found a couple of fixes because despite being a documented bug, there’s not definitive fixes yet.
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Leave a Comment » | Bash (Shell), hacks, Life in the workplace | Tagged: Annoyances, DPMS, Eclipse, Icons, Karmic Kaola, Koala, Moon, screen-saver, screensaver, X, X11 | Permalink
Posted by Steven Pigeon
December 15, 2009
Building a decent personal library is not very difficult but it can be really expensive. It doesn’t have to, you just have to know where to look for.
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2 Comments | algorithms, Books, Life, Mathematics, Science | Tagged: book shops, Dover, Used Books | Permalink
Posted by Steven Pigeon
