\usepackage{amsmath}
\begin{document}
-Here is what resampling we need to do. Content video is at $C_V$ fps, audio at $C_A$.
+Here is what resampling we need to do. Content video is at $C_V$ fps, audio at $C_A$.
\section{Easy case 1}
R_A &= \frac{C_V F_A}{F_V}
\end{align*}
+Once this is done, consider 1 second's worth of content samples ($C_A$
+samples). We have turned them into $R_A$ samples which should still
+last 1 second. These samples are then played back at $F_A$ samples
+per second, so they last $R_A / F_A$ seconds. Hence there is a
+scaling between some content time and some DCP time of $R_A / F_A$
+i.e. $C_V / F_V$.
+
+
+\section{Another explanation}
+
+Say we have some content at a video rate $C_V$ and we want to
+run it at DCP video rate $F_V$. It's always the video rates that
+decide what to do, since we don't have an equivalent to audio
+resampling in the video domain.
+
+We can just mark the video as $F_V$ and it will run $F_V / C_V$ faster
+than it was. Let's call the factor $S = F_V / C_V$.
+
+An equivalent for audio would be to take the content audio at a rate
+$C_A$ and mark it as $C_A S$. Then the same audio frames will be run
+more quickly, just as the same video frames are being. The audio would be
+in sync with the video since it has been sped up by the same amount.
+
+In practice we can't do this, in general, as the only allowed DCP
+audio rates are 48kHz and 96kHz. Instead, we'll resample to some new
+rate $P$ and mark it as $Q$ where $Q / P = S$. Resampling does not
+change the sound, just how many samples are being used to describe it,
+so this is equivalent to marking the original, unsampled audio as $C_A S$.
+
+Then we set $Q = 48$kHz so that $P = 48000 / S$, or $P = C_V F_A
+/ F_V$.
+
+Note that the original sampling rate of the audio content is
+irrelevant. Also, skipping or doubling of video frames is analagous
+to audio resampling: the data are the same, just represented with more
+or fewer samples.
+
\end{document}
projects / dcpomatic.git / blobdiff