Someone with more of a background in signals than I have can verify
this, but I suppose the correct measure of the information capacity of
an LP is given by Shannon-Hartley:

http://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem#Statement_of_the_theorem

If we (generously) take the bandwidth to be 30kHz, we just need to know
the signal/noise for an LP to compute the capacity.  Now we know that
for a CD, the capacity is 44,100*16*2 b/s = 1.4 Mb/s, so to match that
an LP would need a signal/noise ratio of about 10^14 (140 dB), which is
totally unrealistic.  If instead we take a S/N of a million (60 dB), we
get a capacity of .6 Mb/s, or a bit less than half of CD capacity.  

And that's the theoretical best possible capacity given a bandwidth of
30kHz and 60 dB of S/N, both of which are pretty generous assumptions.

So it seems that, at least at the level of theoretical information
capacity, vinyl is considerably worse than CD - which really shouldn't
be a surprise.


-- 
opaqueice
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