Re: Digital Watermarks for copy protection in recent Billbo

At 2:42 PM 7/23/96, Alex F wrote:
>> >  People buying CDs at a garage sale & getting arrested for
>> >piracy.  Wonderful.
>>
>> Arrests like this are uncommon. Even buying "cheap bikes" and other "cheap"
>> (= probably stolen and fenced) merchandise almost never subjects the
>> purchaser to criminal sanctions.
>
>Yes, but concievably if (whoever would be incharge, FBI?) *could*,
>under law do this, even if they are wrong.  It is a lot harder to
>prove that they intentionally harrassed *you* than it is for them to
>say that they were following leads and show evidence.  Yes, this may

To go to trial, an indictment would be needed. How likely is this? Not very.

Discussion of "in theory they could arrest you" points often neglects the
realities of the legal system.

A large fraction of pawnshop items have questionable provenance, the items
having been stolen at some time in the past. Could J. Random Buyer who
walks in, sees an item he likes, buys it, and walks out with it be
handcuffed and taken down the lockup for the crime of buying stolen
property? Doubtful, in the real world. And defense would be ridicuously
easy.


>Cds are often sampled at 48 these days.  Mine was, and we had to
>reduce it to 44.1 for mass producing (much to our surprise, since
>many CD manufacturers love getting stuff at 48 over 44.1)

A trivial increase in frequency, and still not allowing the hypothesized 30
KHz signal to be added. DATs often sample at 44 and 48 KHz, switchably. The
CD standard is of course still what it is.

>Not familiar with the Nyquist limit w/ regards to sampling rate vs
>frequency :(

Check any textbook, or even a good dictionary. Basically, it says that one
must sample at more than twice the frequency of the highest frequency to be
reconstructed. Thus, a 20 KHz top frequency needs at least 40 K samples per
second. The exact number is, I think, about 2.2x the freqency, which is why
CDs were standardized at 44 K samples per second per channel.

--Tim May

Boycott "Big Brother Inside" software!
We got computers, we're tapping phone lines, we know that that ain't allowed.
---------:---------:---------:---------:---------:---------:---------:----
Timothy C. May              | Crypto Anarchy: encryption, digital money,
tcmay@got.net  408-728-0152 | anonymous networks, digital pseudonyms, zero
W.A.S.T.E.: Corralitos, CA  | knowledge, reputations, information markets,
Licensed Ontologist         | black markets, collapse of governments.
"National borders aren't even speed bumps on the information superhighway."

Timothy C. May writes:
> >Not familiar with the Nyquist limit w/ regards to sampling rate vs
> >frequency :(
> 
> Check any textbook, or even a good dictionary. Basically, it says that one
> must sample at more than twice the frequency of the highest frequency to be
> reconstructed. Thus, a 20 KHz top frequency needs at least 40 K samples per
> second. The exact number is, I think, about 2.2x the freqency, which is why
> CDs were standardized at 44 K samples per second per channel.

The Nyquist Theorem states you need exactly twice the samples, not
over twice. The magic number isn't something like 2.2, its exactly
2. Now, the reality is that low pass filters in the recording studio
aren't going to be perfect and such, being analog devices, and higher
frequencies making it in will cause aliasing artifacts, so you
probably want to sample at above twice your putative cutoff because it
won't be your real cutoff, but in principle you need exactly twice the
highest frequency.

Perry

"Perry E. Metzger" <perry@piermont.com> writes:

 > The Nyquist Theorem states you need exactly twice the
 > samples, not over twice. The magic number isn't something
 > like 2.2, its exactly 2.

The Sampling Theorem states that equally spaced instantaneous
samples must be taken at a rate GREATER THAN twice the highest
frequency present in the analog signal being sampled.  If this is
done, the samples contain all the information in the signal, and
faithful reconstruction is possible.

Exactly twice the highest frequency won't do, and it should be
obvious that sampling a sine wave at twice its frequency yields
samples of constant magnitude and alternating sign which convey
nothing about its phase and little useful about its amplitude
either.  (Drawing a little picture might be helpful here.)

Although anything over twice the highest frequency will work in a
theoretical sense, a small fudge factor does wonders for digital
signal processing, if only to reduce to a reasonable value the
width of the window into the sample stream needed for various
signal manipulations.

--
     Mike Duvos         $    PGP 2.6 Public Key available     $
     mpd@netcom.com     $    via Finger.                      $

Mike Duvos writes:
> "Perry E. Metzger" <perry@piermont.com> writes:
>  > The Nyquist Theorem states you need exactly twice the
>  > samples, not over twice. The magic number isn't something
>  > like 2.2, its exactly 2.
> 
> The Sampling Theorem states that equally spaced instantaneous
> samples must be taken at a rate GREATER THAN twice the highest
> frequency present in the analog signal being sampled.

That is just about what I said. The point is that the magic number
isn't 2.2 or anything similar -- the breakpoint is exactly twice the
frequency.

> Although anything over twice the highest frequency will work in a
> theoretical sense, a small fudge factor does wonders for digital
> signal processing,

I believe I mentioned the need for that, too.

Perry